Within the class of Tychonoff spaces, and within the class of topological groups, most of the natural questions concerning ‘productive closure’ of the subclasses of countably compact and pseudocompact spaces are answered by the following three well-known results: (1) [ZFC] There is a countably compact Tychonoff space X such that X XX is not pseudocompact; (2) [ZFC] The product of any set of pse...

In this paper, we consider a new secure spatial modulation scenario with full-duplex (FD) malicious attacker Mallory owning eavesdropping capacity, where works on FD model and transmits jamming such as artificial noise (AN) to interfere legitimate user Bob. To suppress the Bob from Mallory, conventional maximum receive power (Max-RP) at is presented firstly. Subsequently, exploit colored proper...

The magnetic field induced martensitic transformation (MT) and its arrest exhibited by the prototype Ni-Mn-In metamagnetic shape memory alloy have been studied for two distinct states achieved different cooling routes, namely, a zero (ZFC) strong (SFC). For that, magnetization as function of up to 33 T was measured at constant temperatures. As result, phase diagrams “MT versus temperature” were...

The existence of an אω+1-Dowker space is proved in ZFC using pcf theory.

We prove, in ZFC, the existence of a definable, countably saturated elementary extension of the reals.

Cantor’s Continuum Hypothesis was proved to be independent from the usual ZFC axioms of Set Theory by Gödel and Cohen. The method of forcing, developed by Cohen to this end, has lead to a profusion of independence results in the following decades. Many other statements about infinite sets, such as the Borel Conjecture, Whitehead’s problem, and automatic continuity for Banach Algebras, were prov...

A nonstandard set theory ∗ZFC is proposed that axiomatizes the nonstandard embedding ∗. Besides the usual principles of nonstandard analysis, all axioms of ZFC except regularity are assumed. A strong form of saturation is also postulated. ∗ZFC is a conservative extension of ZFC. Introduction. For practitioners, the most popular foundational approach to nonstandard methods is the so-called super...

It is proved undecidable in ZFC + GCH whether every Z-module has a {Z}-precover. Let F be a class of R-modules of the form C = {A : Ext(A,C) = 0 for all C ∈ C} for some class C. The first author and Jan Trlifaj proved [7] that a sufficient condition for every module M to have an F -precover is that there is a module B such that F = {B} (= {A : Ext(B,A) = 0}). In [8], generalizing a method used ...