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On pseudocompactness and related notions in ZF

Kyriakos Keremedis (2018)

Commentationes Mathematicae Universitatis Carolinae

We study in ZF and in the class of T 1 spaces the web of implications/ non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC equivalents.

On reflection of stationary sets

Q. Feng, Menachem Magidor (1992)

Fundamenta Mathematicae

We show that there are stationary subsets of uncountable spaces which do not reflect.

On reverses of some binary operators

Michal Šabo, Peter Strežo (2005)

Kybernetika

The notion of reverse of any binary operation on the unit interval is introduced. The properties of reverses of some binary operations are studied and some applications of reverses are indicated.

On rigid relation principles in set theory without the axiom of choice

Paul Howard, Eleftherios Tachtsis (2016)

Fundamenta Mathematicae

We study the deductive strength of the following statements: 𝖱𝖱: every set has a rigid binary relation, 𝖧𝖱𝖱: every set has a hereditarily rigid binary relation, 𝖲𝖱𝖱: every set has a strongly rigid binary relation, in set theory without the Axiom of Choice. 𝖱𝖱 was recently formulated by J. D. Hamkins and J. Palumbo, and 𝖲𝖱𝖱 is a classical (non-trivial) 𝖹𝖥𝖢-result by P. Vopěnka, A. Pultr and Z. Hedrlín.

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