Publications:
1. Ε. Tachtsis (with Κ. Keremedis), On the extensibility of closed filters in T1 spaces and the existence of well orderable filter bases, Commentationes Math. Universitatis Carolinae, 40 (2), (1999), 343-353.
2. Ε. Tachtsis (with Κ. Keremedis), Non-constructive properties of well-ordered T2 topological spaces, Notre Dame Journal of Formal Logic, 40 (4), (1999), 548-553.
3. Ε. Tachtsis (with Κ. Keremedis), On Lindelöf Metric Spaces and Weak Forms of the Axiom of Choice, Mathematical Logic Quarterly, 46 (1), (2000), 35-44.
4. Ε. Tachtsis (with Κ. Keremedis), Compact Metric Spaces and Weak Forms of the Axiom of Choice, Mathematical Logic Quarterly, 47 (1), (2001), 117-128.
5. Ε. Tachtsis (with P. Howard, Κ. Keremedis, J. E. Rubin and A. Stanley), Non-constructive properties of the real numbers, Mathematical Logic Quarterly, 47 (3), (2001), 423-431.
6. Ε. Tachtsis (with Κ. Keremedis), Some weak forms of the axiom of choice restricted to the real line, Mathematical Logic Quarterly, 47 (3), (2001), 413-422.
7. Ε. Tachtsis (with Κ. Keremedis), On Loeb and weakly Loeb Hausdorff spaces, Scientiae Mathematicae Japonicae, 53 (2), (2001), 247-251.
8. Ε. Tachtsis, Disasters in Metric Topology without Choice, Commentationes Math. Universitatis Carolinae, 43 (1), (2002), 165-174.
9. Ε. Tachtsis (with H. Herrlich and Κ. Keremedis), Striking Differences between ZF and ZF + Weak Choice in view of Metric Spaces, Quaestiones Mathematicae 25 (2002), 405-420.
10. Ε. Tachtsis (with Κ. Keremedis), Choice principles for special subsets of the real line, Math. Logic Quarterly, 49 (5), (2003), 444-454.
11. Ε. Tachtsis (with Κ. Keremedis), On sequentially compact subspaces of R without the axiom of choice, Notre Dame Journal of Formal Logic Vol. 44, No. 3 (2003), 175-184.
12. Ε. Tachtsis (with Κ. Keremedis), Topology in the absence of the axiom of choice, Scientiae Mathematicae Japonicae, 59, No. 2 (2004), 357-406.
13. Ε. Tachtsis (with Κ. Keremedis), Countable Sums and Products of Metrizable Spaces in ZF, Math. Logic Quarterly, Vol. 51, No.1 (2005), 95-103.
14. Ε. Tachtsis (with Κ. Keremedis), Weak Axioms of Choice for Metric Spaces, Proceedings of the American Mathematical Society, 133 (2005), no.12, 3691-3701.
15. Ε. Tachtsis (with H. Herrlich and Κ. Keremedis), Countable Sums and Products of Loeb and Selective Metric Spaces, Commentationes Math. Universitatis Carolinae, 46, No. 2 (2005), 373-384.
16. Ε. Tachtsis (with O. De la Cruz, E. Hall, P. Howard and Κ. Keremedis), Properties of the Real Line and Weak Forms of the Axiom of Choice, Math. Logic Quarterly, Vol. 51, 6 (2005), 598-609.
17. Ε. Tachtsis (with Κ. Keremedis), Countable compact Hausdorff spaces need not be metrizable in ZF, Proceedings of the American Mathematical Society 135 (2007), no. 4, 1205-1211.
18. Ε. Tachtsis, (with Κ. Keremedis and Ε. Felouzis) Countable Compact Scattered T2 Spaces and Weak Forms of AC, Bulletin of the Polish Academy of Sciences, Vol. 54, No. 1 (2006), 75-84.
19. Ε. Tachtsis (with H. Herrlich), On the number of Russell's socks or 2+2+2+… = ?, Commentationes Math. Univ. Carolinae, 47, 4 (2006) 707-717.
20. Ε.Tachtsis, (with Κ. Keremedis and Ε. Felouzis), On the Compactness and Countable Compactness of 2R in ZF, Bull. Polish Acad. Sci. Math. 55 (2007), 293-302.
21. Ε. Tachtsis, An Independence Result Concerning Russell-Cardinals, Quaestiones Mathematicae 31 (2008), 173-177.
22. Ε. Tachtsis (with H. Herrlich, Κ. Keremedis), Tychonoff Products of Super Second Countable and Super Separable Metric Spaces, Cahiers Topologie Geom. Differentielle Categoriques 49 (2008), 267-279.
23. Ε. Tachtsis (with H. Herrlich, Κ. Keremedis), Οn Super Second Countable and Super Separable Metric Spaces, Topology Proceedings 33 (2009), 239-249.
24. Ε. Tachtsis (with Κ. Keremedis), Different versions of a first countable space without choice, Topology and its Applications 156 (2009), 2000-2004.
25. Ε. Tachtsis (with H. Herrlich), Odd-Sized Partitions of Russell-Sets, Math. Logic Quart. Vol. 56 No. 2 (2010), 185-190.
26. Ε. Tachtsis (with H. Herrlich, K. Keremedis), On Russell and anti Russell-cardinals, Quaestiones Math. Vol. 33 (2010), 1-9.
27. Ε. Tachtsis (with Κ. Keremedis), Products of some special compact spaces and restricted forms of AC, The Journal of Symbolic Logic Vol. 75 Issue 3 (2010), 996-1006.
28. Ε. Tachtsis, On the Set-Theoretic Strength of Countable Compactness of the Tychonoff Product 2R, Bulletin of the Polish Academy of Sciences Mathematics Vol. 58 No. 2 (2010), 91-107
29. Ε. Tachtsis (with Κ. Keremedis), Extensions of Compactness of Tychonoff Powers of 2 in ZF, Topology Proceedings 37 (2011), 15-31.
30. Ε. Tachtsis (with H. Herrlich, P. Howard), The cardinal inequality a2<2a, Quaestiones Math., 34(1) (2011), 35-66.
31. Ε. Tachtsis (with H. Herrlich, K. Kερεμίδη), Remarks on the Stone spaces of the integers and the reals without AC, Bulletin of the Polish Academy of Sciences Mathematics 59 No.2 (2011), 101-114.
32. Ε. Tachtsis, BPI is equivalent to compactness-n, n>= 6, of Tychonoff powers of 2, Topology Proceedings Vol. 40 (2012), 21-28.
33. Ε. Tachtsis (with H. Herrlich, P. Howard), On Special Partitions of Dedekind- and Russell-Sets, Comment. Math. Univ. Carolinae 53, 1 (2012), 105-122.
34. Ε. Tachtsis (with E. J. Hall, Κ. Keremedis), The existence of free ultrafilters on ω does not imply the extension of filters on ω to ultrafilters, Math. Logic Quarterly,59 Issue 4-5 (2013), 258-267.
35. Ε. Tachtsis (with P. Howard), On Vector Spaces Over Specific Fields Without Choice, Math. Logic Quarterly, 59, Νο. 3 (2013), 128-146.
36. Ε. Tachtsis (with K. Keremedis), Wallman Compactifications and Tychonoff’s Compactness Theorem in ZF, Topology Proceedings 42 (2013), 275-297.
37. Ε. Tachtsis (with P. Howard), On a topological choice principle by Murray Bell, Topology and its Applications, Elsevier, 160, Issue 2 (2013), 309-327.
38. Ε. Tachtsis (with P. Howard), On a variant of Rado's selection lemma and its equivalence with the Boolean prime ideal theorem, Archive for Mathematical Logic, Springer, 53, Issue 7 (2014), 825-833.
39. Ε. Tachtsis, Variants of the Principle of Dependent Choices and a Topological Proposition, Questions and Answers in General Topology, Part A (Answers), 32 (2014), 53-62.
40. Ε. Tachtsis (with P. Howard), On the Minimal Cover Property in ZF, Topology and its Applications, Elsevier, 173 (2014), 94-106.
41. Ε. Tachtsis, On the Existence of Free Ultrafilters on ω and on Russell-sets in ZF, Bulletin Polish Acad. Sci. Math. 63 No.1 (2015), 1-10.
42. Ε. Tachtsis (with H. Herrlich and P. Howard), On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice, Bulletin of the Polish Academy of Sciences, Mathematics Vol. 63, No. 2 (2015), 89-112.
43. Ε. Tachtsis (with P. Howard), On rigid relation principles in set theory without the axiom of choice, Fundamenta Mathematicae 232 No.3 (2016), 199-226.
44. Ε. Tachtsis (with H. Herrlich and P. Howard), Finiteness Classes and Small Violations of Choice, Notre Dame Journal of Formal Logic 57, Number 3 (2016), 375-388.
45. Ε. Tachtsis (with P. Howard and D. I. Saveliev), On the set-theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements, Math. Logic Quarterly (Wiley-VCH) 62, Issue 3 (2016), 155-176.
46. Ε. Tachtsis (with P. Howard), No Decreasing Sequence of Cardinals, Archive for Mathematical Logic (Springer) 55, Issue 3-4 (2016), 415-429.
47. Ε. Tachtsis (with P. Howard), On the set-theoretic strength of the n-compactness of generalized Cantor cubes, Fundamenta Mathematicae 234 (2016), 241-252.
48. Ε. Tachtsis, On Martin’s Axiom and Forms of Choice, Mathematical Logic Quarterly (Wiley-VCH) 62, Issue 3 (2016), 190-203.
49.
Ε.
Τachtsis,
On Ramsey’s Theorem and the existence of infinite chains or infinite
anti-chains in infinite posets, The Journal of Symbolic Logic
(Cambridge University Press) 81, Issue 01 (2016), 384 – 394.
50.
Ε. Τachtsis,
On variants of the principle of consistent choices, the minimal cover property and the 2-compactness of generalized Cantor cubes, Topology and its Applications (Elsevier) 219 (2017), 122-140.
52. Ε. Tachtsis (with P. Howard), On Infinite-Dimensional Banach Spaces and Weak Forms of the Axiom of Choice, Mathematical Logic Quarterly 63 (2017), 509-535.
53. Ε. Τachtsis (with M. Di Nasso), Idempotent ultrafilters without Zorn’s Lemma, Proceedings of the American Mathematical Society 146 (2018), no. 1, 397-411.
54. Ε. Τachtsis, On the Minimal Cover Property and Certain Notions of Finite, Archive for Mathematical Logic (Springer) 57 (2018), no. 5-6, 665-686.
55. Ε. Τachtsis, A Note on the Deductive Strength of the Nielsen-Schreier Theorem, Mathematical Logic Quarterly (Wiley-VCH) 64 (2018), no. 3, 173-177.
56. Ε. Τachtsis, On the comparability of cardinals in the absence of the Axiom of Choice, Fundamenta Mathematicae 242 (2018), no. 3, 247-266.
57. Ε. Tachtsis, On the set-theoretic strength of Ellis’ Theorem and the existence of free idempotent ultrafilters on ω, The Journal of Symbolic Logic 83 (2018), no. 2, 551-571.
58. Ε. Tachtsis, On certain non-constructive properties of infinite-dimensional vector spaces, Commentationes Mathematicae Universitatis Carolinae 59, 3 (2018), 285-309.
59. Ε. Tachtsis, Łoś’s theorem and the axiom of choice, Mathematical Logic Quarterly (Wiley-VCH) 65, No. 3 (2019), 280-292.
60. Ε. Tachtsis, On the existence of permutations of infinite sets without fixed points in set theory without choice, Acta Mathematica Hungarica (Springer) 157 (2) (2019), 281-300.
61. Ε. Tachtsis, On H-closed and Minimal Hausdorff Spaces and the Boolean Prime Ideal Theorem, Topology Proceedings 53 (2019), 255-268.
62. Ε. Tachtsis, Dilworth's decomposition theorem for posets in ZF, Acta Mathematica Hungarica (Springer) 159 (2) (2019), 603-617.
63. Ε. Tachtsis, The Urysohn Lemma is independent of ZF + Countable Choice, Proceedings of the American Mathematical Society 147, Number 9 (2019), 4029-4038.
64. Ε. Tachtsis, On the existence of almost disjoint and MAD families without AC, Bulletin of the Polish Academy of Sciences, Mathematics 67, No. 2 (2019), 101-124.
65. E. Tachtsis, On ultracompact spaces in ZF, Topology and its Applications (Elsevier) 263 (2019), 257-278.
66. E. Tachtsis, Infinite Hausdorff spaces may lack cellular families or discrete subsets of cardinality $\aleph_{0}$, Topology and its Applications (Elsevier) 275 (2020), 106997, 19pp.
67. Ε. Tachtsis (with Κ. Keremedis), Cellularity of Infinite Hausdorff Spaces in ZF, Topology and its Applications (Elsevier) 274 (2020), 107104, 20pp.
68. E. Tachtsis (with L. Halbeisen), On Ramsey Choice and Partial Choice for infinite families of n-element sets, Archive for Mathematical Logic (Springer) 59 (2020), 583-606.
69. E. Tachtsis (with P. Howard), On the set-theoretic strength of a topological Banach fixed point theorem for continua, Topology Proceedings 55 (2020), 295-313.
70. E. Tachtsis, Juh\'{a}sz's topological generalization of Neumer's theorem may fail in ZF, Proceedings of the American Mathematical Society 148 (2020), no. 3, 1295-1310.
71. E. Tachtsis, The Boolean prime ideal theorem does not imply the extension of almost disjoint families to MAD families, Bulletin of the Polish Academy of Sciences, Mathematics 68, No. 2 (2020), 105-115.
72. E. Tachtsis (with P. Howard), On metrizability and compactness of certain products without the Axiom of Choice, Topology and its Applications (Elsevier) 290 (2021), 107591.
73. E. Tachtsis (with K. Keremedis and E. Wajch), Second-countable compact Hausdorff spaces as remainders in ZF and two new notions of infiniteness, Topology and its Applications (Elsevier) 298 (2021), 107732.
74. E. Tachtsis (with K. Keremedis and E. Wajch), Several results on compact metrizable spaces in ZF, Monatshefte für Mathematik (Springer) 196 (2021), 67-102.
75. E. Tachtsis, MA($\aleph_{0}$) restricted to complete Boolean algebras and choice, Mathematical Logic Quarterly (Wiley-VCH) 67, No. 4 (2021), 420-431.
76. E. Tachtsis (with J. Hejduk and E. Wajch), On Urysohn's Lemma for Generalized Topological Spaces in ZF, Results in Mathematics (Springer/Birkhäuser) 77 (2022), 19pp.
77. E. Tachtsis, On the interrelation of a theorem of Juh\'{a}sz and certain weak axioms of choice, Fundamenta Mathematicae 256, no. 3 (2022), 261-283.
78. E. Tachtsis, Almost Disjoint and MAD Families in Vector Spaces and Choice Principles, The Journal of Symbolic Logic (Cambridge) 87, No. 3 (2022), 1093-1110.
79. E. Tachtsis, Some independence results about compact metrizable spaces and two notions of finiteness, Topology and its Applications (Elsevier) 307 (2022), 107947.
80. E. Tachtsis (with K. Keremedis), Stranger things about the cardinality of compact metric spaces without AC, Acta Mathematica Hungarica (Springer) 168, no. 1 (2022), 269-294.
81. E. Tachtsis, Hindman's Theorem and Choice, Acta Mathematica Hungarica (Springer) 168, no. 2 (2022), 402-424.
82. E. Tachtsis, On a theorem of Kurepa for partially ordered sets and weak choice, Monatshefte für Mathematik (Springer) 199, no. 3 (2022), 645-669.
83. E. Tachtsis (with K. Keremedis and E. Wajch), Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice, Annals of Pure and Applied Logic (Elsevier) 174 (2023), no. 7, 103283, 34pp.
84. E. Tachtsis (with K. Keremedis and E. Wajch), On Iso-dense and Scattered Spaces without AC, Results in Mathematics (Springer/Birkhäuser) (2023), no. 4, Paper No. 153, 30pp.
85. E. Tachtsis (with P. Howard), Models of ZFA in which every linearly ordered set can be well ordered, Archive for Mathematical Logic (Springer) 62 (2023), 1131-1157.
86. E. Tachtsis (with K. Keremedis), On Hausdorff operators in ZF, Mathematical Logic Quarterly (Wiley-VCH) 69 (2023), 347-369.
87. E. Tachtsis, On Some Open Problems about P-Spaces, Strongly Quasi Baire Spaces and Choice, Results in Mathematics (Springer/Birkhäuser) 79 (2024), Paper No. 19, 24pp.
88. E. Tachtsis, On the deductive strength of the Erdős-Dushnik-Miller theorem and two order-theoretic principles, Monatshefte für Mathematik (Springer) 203 (2024), 677-693.
89. E. Tachtsis, On two theorems of Arens-Dugundji and Scott-Watson-Förster without the Axiom of Choice, accepted in Topology and its Applications (Elsevier).
90. E. Tachtsis, No Decreasing Sequence of Cardinals in the Hierarchy of Choice Principles, Notre Dame Journal of Formal Logic 65 (2024), no. 3, 311-331.
91. E. Tachtsis, Ellis' theorem, minimal left ideals, and minimal/maximal idempotents without AC, Acta Mathematica Hungarica (Springer) 174 (2024), no. 2, 545-569.
92. E. Tachtsis, On free ultrafilters on ω with well-orderable bases in ZF, accepted in The Journal of Symbolic Logic (Cambridge).
93. E. Tachtsis, On consequences of the Countable Union Theorem, their deductive strength and interaction with topology, Fundamenta Mathematicae 268 (2025), no. 3, 235-284.
94. E. Tachtsis, Metric spaces in choiceless set theory, Annals of Pure and Applied Logic (Elsevier) 176 (2025) 103603.
95. E. Tachtsis, Divisibility vs. Strong Divisibility in Set Theory Without AC, accepted in Periodica Mathematica Hungarica (Springer).