Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A parallel to the null ideal for inaccessible lambda. Part I   It is well known to generalize the meagre ideal replacing aleph_0 by a
(regular) cardinal lambda > aleph_0 and requiring the ideal to be
lambda^+-complete. But can we generalize the null ideal? In terms of forcing,
this means finding a forcing notion similar to the random real forcing,
replacing aleph_0 by lambda, so requiring it to be (<lambda)-complete. Of
course, we would welcome additional properties generalizing the ones of the
random real forcing. Returning to the ideal (instead forcing) we may look at
the Boolean Algebra of lambda-Borel sets modulo the ideal. Surprisingly we get
an positive = existence answer for lambda a "mild" large cardinals: the weakly
compact ones. We apply this to get consistency results on cardinal invariants
for such lambda's. We shall deal with other cardinals more properties related
forcing notions in a continuation.

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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con