摘要: In classical computability theory, a recursive counterexample to theorem shows that the latter does not hold when restricted computable objects. These counterexamples are highly useful in Reverse Mathematics program, where aim of is determine minimal axioms needed prove given ordinary mathematics. Indeed, often (help) establish 'reverse' implication typical equivalence between said and at hand. The aforementioned generally formulated language second-order arithmetic. this paper, we show readily modified provide similar implications higher-order For instance, analogue 'sequence' topological notion 'net', also known as 'Moore-Smith sequence'. Finally, our results on metric spaces suggest can only be reasonably studied weak systems via representations (aka codes)
arxiv.org参考文章(17)
Walter Rudin, Real and complex analysis, 3rd ed. McGraw-Hill, Inc.. ,(1987)
Charles Swartz, Introduction to Gauge Integrals ,(2001)
Horst Herrlich, Axiom of Choice ,(2006)
Pierre Cousin, Sur les fonctions de n variables complexes Acta Mathematica. ,vol. 19, pp. 1- 61 ,(1895) , 10.1007/BF02402869
Harvey M. Friedman, Stephen G. Simpson, Rick L. Smith, Countable algebra and set existence axioms Annals of Pure and Applied Logic. ,vol. 25, pp. 141- 181 ,(1983) , 10.1016/0168-0072(83)90012-X
Thomas J. Jech, The axiom of choice ,(1973)
P. Muldowney, A general theory of integration in function spaces : including Wiener and Feynman integration Longman Scientific & Technical , Wiley. ,(1987)
Ernst Specker, Nicht Konstruktiv Beweisbare Sätze der Analysis Ernst Specker Selecta. ,vol. 14, pp. 35- 48 ,(1990) , 10.1007/978-3-0348-9259-9_2
G. Kreisel, A.S. Troelstra, Formal systems for some branches of intuitionistic analysis Annals of Mathematical Logic. ,vol. 1, pp. 229- 387 ,(1970) , 10.1016/0003-4843(70)90001-X
Kostas Hatzikiriakou, Minimal prime ideals and arithmetic comprehension Journal of Symbolic Logic. ,vol. 56, pp. 67- 70 ,(1991) , 10.2307/2274904