Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Possible Size of an ultrapower of omega   Let omega be the first infinite ordinal (or the set of all natural numbers)
with the usual order <. In section 1 we show that, assuming the consistency of
a supercompact cardinal, there may exist an ultrapower of omega, whose
cardinality is (1) a singular strong limit cardinal, (2) a strongly
inaccessible cardinal. This answers two questions in [CK], modulo the
assumption of supercompactness. In section 2 we construct several
lambda-Archimedean ultrapowers of omega under some large cardinal assumptions.
For example, we show that, assuming the consistency of a measurable cardinal,
there may exist a lambda-Archimedean ultrapower of omega for some uncountable
cardinal lambda. This answers a question in [KS], modulo the assumption of
measurability.

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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: eess