Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Definably amenable groups in Continuous logic   We generalize the notions of definable amenability and extreme definable
amenability to continuous structures and show that the stable and ultracompact
groups are definable amenable. In addition, we characterize both notions in
terms of fixed-point properties. We prove that, for dependent theories,
definable amenability is equivalent to the existence of a good S1 ideal.
Finally, we show the randomizations of first-order definable amenable groups
are extreme definably amenable.

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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas