المؤلفون: Herrlich, Horst, Tachtsis, Eleftherios

مصطلحات موضوعية: keyword:Axiom of Choice, keyword:weak axioms of choice, keyword:linear equations with coefficients in $\mathbb{Z}$, keyword:infinite systems of linear equations over $\mathbb{Z}$, keyword:non-trivial solution of a system in $\mathbb{Z}$, keyword:permutation models of $\mathsf{ZFA}$, keyword:symmetric models of $\mathsf{ZF}$, msc:03E25, msc:03E35

وصف الملف: application/pdf

Relation: mr:MR3666944; zbl:Zbl 06773717; reference:[1] Abian A.: Generalized completeness theorem and solvability of systems of Boolean polynomial equations.Z. Math. Log. Grundlagen Math. 16 (1970), 263–264. Zbl 0202.00704, MR 0277450, 10.1002/malq.19700160306; reference:[2] Blass A.: Ramsey's theorem in the hierarchy of choice principles.J. Symbolic Logic 42 (1977), 387–390. Zbl 0374.02037, MR 0465865, 10.2307/2272866; reference:[3] Herrlich H.: Axiom of Choice.Lecture Notes in Mathematics, 1876, Springer, Berlin, 2006. Zbl 1102.03049, MR 2243715; reference:[4] Howard P., Rubin J.E.: The axiom of choice for well-ordered families and for families of well-orderable sets.J. Symbolic Logic 60 (1995), no. 4, 1115–1117. Zbl 0848.03026, MR 1367198, 10.2307/2275876; reference:[5] Howard P., Rubin J.E.: Consequences of the Axiom of Choice.Mathematical Surveys and Monographs, 59, American Mathematical Society, Providence, RI, 1998. Zbl 0947.03001, MR 1637107, 10.1090/surv/059; reference:[6] Howard P., Solski J.: The strength of the $\Delta$-system lemma.Notre Dame J. Formal Logic 34 (1993), no. 1, 100–106. Zbl 0781.03037, MR 1213850, 10.1305/ndjfl/1093634567; reference:[7] Howard P., Tachtsis E.: On vector spaces over specific fields without choice.Math. Log. Quart. 59 (2013), no. 3, 128–146. Zbl 1278.03082, MR 3066735, 10.1002/malq.201200049; reference:[8] Jech T.J.: The Axiom of Choice.Studies in Logic and the Foundations of Mathematics, 75, North-Holland, Amsterdam, 1973; reprint: Dover Publications, Inc., New York, 2008. Zbl 0259.02052, MR 0396271; reference:[9] Jech T.J.: Set Theory.The third millennium edition, revised and expanded, Springer Monographs in Mathematics, Springer, Berlin, Heidelberg, 2003. Zbl 1007.03002, MR 1940513; reference:[10] Kunen K.: Set Theory. An Introduction to Independence Proofs.Studies in Logic and the Foundations of Mathematics, 102, North-Holland, Amsterdam, 1980. Zbl 0534.03026, MR 0597342

الاتاحة: http://hdl.handle.net/10338.dmlcz/146791

المؤلفون: Herrlich, Horst, Keremedis, Kyriakos

مصطلحات موضوعية: keyword:weak axioms of choice, keyword:pseudometric spaces, keyword:metric reflections, keyword:complete metric and pseudometric spaces, keyword:limit point compact, keyword:Alexandroff-Urysohn compact, keyword:ultrafilter compact, keyword:sequentially compact, msc:54E35, msc:54E45

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/144190

المؤلفون: Herrlich, Horst, Keremedis, Kyriakos, Tachtsis, Eleftherios

مصطلحات موضوعية: keyword:axiom of choice, keyword:weak axioms of choice, keyword:Loeb metric spaces, keyword:selective metric spaces, keyword:countable Tychonoff products of metric spaces, keyword:countable sums of metric spaces, msc:03E25, msc:54A35, msc:54D45, msc:54E50, msc:54E99

وصف الملف: application/pdf

Relation: mr:MR2176899; zbl:Zbl 1121.03063; reference:[1] Herrlich H., Strecker G.E.: When is $\Bbb N$ Lindelöf?.Comment. Math. Univ. Carolinae 38 (1998), 553-556. MR 1485075; reference:[2] Howard P., Rubin J.E.: Consequences of the Axiom of Choice.Amer. Math. Soc., Math. Surveys and Monographs, Vol. 59, Providence (RI), 1998. Zbl 0947.03001, MR 1637107; reference:[3] Jech T.: The Axiom of Choice.North-Holland, Amsterdam, 1973. Zbl 0259.02052, MR 0396271; reference:[4] Keremedis K.: The failure of the axiom of choice implies unrest in the theory of Lindelöf metric spaces.Math. Log. Quart. 49 2 (2003), 179-186. Zbl 1016.03051, MR 1961460; reference:[5] Kelley J.: The Tychonoff product theorem implies the axiom of choice.Fund. Math. 37 (1950), 75-76. Zbl 0039.28202, MR 0039982; reference:[6] Keremedis K.: Consequences of the failure of the axiom of choice in the theory of Lindelöf metric spaces.Math. Log. Quart. 50 2 (2004), 1-11. Zbl 1041.54022, MR 2037733; reference:[7] Keremedis K., Tachtsis E.: On Lindelöf metric spaces and weak forms of the axiom of choice.Math. Log. Quart. 46 (2000), 35-44. Zbl 0952.03060, MR 1736648; reference:[8] Keremedis K., Tachtsis E.: Compact metric spaces and weak forms of the axiom of choice.Math. Log. Quart. 47 (2001), 117-128. Zbl 0968.03057, MR 1808950; reference:[9] Keremedis K., Tachtsis E.: On Loeb and weakly Loeb Hausdorff spaces.Sci. Math. Jpn. 53 (2001), 247-251. Zbl 0982.54001, MR 1828263; reference:[10] Keremedis K., Tachtsis E.: Some weak forms of the axiom of choice restricted to the real line.Math. Log. Quart. 47 (2001), 413-422. Zbl 1001.03044, MR 1847457; reference:[11] Keremedis K., Tachtsis E.: Countable sums and products of metrizable spaces in ZF.Math. Log. Quart. 51 1 (2005), 95-103. Zbl 1059.03048, MR 2099390; reference:[12] Keremedis K., Tachtsis E.: Topology in the absence of the axiom of choice.Sci. Math. Jpn. 59 2 (2004), 357-406. Zbl 1066.54002, MR 2062202; reference:[13] Keremedis K., Tachtsis E.: Weak axioms of choice for metric spaces.to appear in Proc. Amer. Math. Soc. Zbl 1090.03021, MR 2163609; reference:[14] Kunen K.: Set Theory. An Introduction to Independence Proofs.North-Holland, Amsterdam, 1983. Zbl 0534.03026, MR 0756630; reference:[15] Loeb P.A.: A new proof of the Tychonoff theorem.Amer. Math. Monthly 72 (1965), 711-717. Zbl 0146.18404, MR 0190896; reference:[16] Tachtsis E.: Disasters in metric topology without choice.Comment. Math. Univ. Carolinae 43 1 (2002), 165-174. Zbl 1072.03030, MR 1903316; reference:[17] Willard S.: General Topology.Addison-Wesley Publ. Co., Reading, 1970. Zbl 1052.54001, MR 0264581

الاتاحة: http://hdl.handle.net/10338.dmlcz/119531