Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maker-Breaker games on $ K_{\omega_1}$ and $K_{\omega,\omega_1}$   We investigate Maker-Breaker games on graphs of size $\aleph_1$ in which
Maker's goal is to build a copy of the host graph. We establish a firm
dependence of the outcome of the game on the axiomatic framework. Relating to
this, we prove that there is a winning strategy for Maker in the
$K_{\omega,\omega_1}$-game under ZFC+MA+$\neg$CH and a winning strategy for
Breaker under ZFC+CH. We prove a similar result for the $K_{\omega_1}$-game.
Here, Maker has a winning strategy under ZF+DC+AD, while Breaker has one under
ZFC+CH again.

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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an