Tagged Questions

Descriptive Set Theory is the study of definable subsets of Polish spaces, where definable is taken to mean from the Borel or projective hierarchies. Other topics include infinite games and determinacy, definable equivalence relations and Borel reductions between them, Polish groups, and effective ...

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About the axiom of choice, the fundamental theorem of algebra, and real numbers

About fundamental theorem of algebra, there is a large collection different demonstrations. I ask: is there some proof that avoids AC (choice axiom)? In a general topos (with natural number object) ...
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Indeterminacy of long games

Hello, all, Several months ago I sat in on a seminar on AD+, which was incredibly wonderful even though I could barely follow it at all. AD+ is a technical variant of AD, the axiom of determinacy, ...
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Kunen tree and Martin tree

Do we know under which conditions the Kunen tree (Recall the Kunen tree provides an analysis of the equivalence classes of functions $f: \omega_1 \to \omega_1$ with respect to the normal measure ...
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Is every sigma-algebra the Borel algebra of a topology?

This question arises from the excellent question posed on math.SE by Salvo Tringali, namely, Correspondence between Borel algebras and topology. Since the question was not answered there after some ...
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Do all possible trees arise as orbit trees of some permutation groups?

I.Motivation from descriptive set theory (Contains some quotes from Maciej Malicki's paper.) The classical theorem of Birkhoff-Kakutani implies that every metrizable topological group G admits a ...
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Choice function on the countable subsets of the reals

It is easy to find a choice function on all finite subsets of $\mathbb R$, but without using the axiom of choice, not on all subsets. Is there an "explicit" choice function on the countable subsets of ...
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Parts of Set Theory immune to independence

The motivation for asking this question is a passage (3.2) in an article by Greg Hjorth where he said that "...it is also an attractive feature of the theory of Borel cardinalities and of the theory ...
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Wanted: chain of nowhere dense subsets of the real line whose union is nonmeagre, or even contains intervals

Let $X$ be a topological space. When I call a set nowhere dense, meagre or similar without qualification, I mean that it has this property as a subset of $X$. Call a subset of $X$ weager (for weakly ...
In John Steel's paper "The derived model theorem", http://math.berkeley.edu/~steel/papers/dm.ps John Steel asserts that it is clear that $\mathrm{Hom}^{Y}_{\kappa}$ is closed downward under ...