1 - 7 of 7 articles
If there is a homeomorphic embedding of one set into another, the sets are said to be topologically comparable. Friedman and Hirst have shown that the topological comparability of countable closed subsets of the reals is equivalent to the subsystem of second order arithmetic denoted byATR
For each completion of Peano Arithmetic there is a weakly definable type which is not definable.
We show an axiom A such that there is no nontrivial interpretation of the alternative set theory (AST) inAST+A keeping ∈, sets and the class of all “standard” natural numbers. Furthermore, there is no interpretation ofAST inAST without the prolongation axiom, but there is an interpretation ofAST...
We define and investigate constructibility in higher order arithmetics. In particular we get an interpretation ofn-order arithmetic inn-order arithmetic without the scheme of choice such that ∈ and the property “to be a well-ordering” are absolute in it and such that this interpretation is...
We show that an infinite field is interpretable in a stable torsion-free nilpotent groupG of classk, k>1. Furthermore we prove thatG/Z
(G) must be divisible. By generalising methods of Belegradek we classify some stable torsion-free nilpotent groups modulo isomorphism and elementary...
This paper will define a new cardinal called aStationary Cardinal. We will show that every weakly∏
-indescribable cardinal is a stationary cardinal, every stationary cardinal is a greatly Mahlo cardinal and every stationary set of a stationary cardinal reflects. On the other hand, the...
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