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Applications of cohomology to questions in set theory i: hausdorff gaps
[article]

1993
*
arXiv
*
pre-print

The

arXiv:math/9311205v1
fatcat:tmwtogf3rzapdmc2w3ol3krfsy
*cohomology**theory*is introduced with enough generality*to*be*applicable**to*other questions in*set**theory*. ... We explore an*application**of*homological algebra*to**set*theoretic objects by developing a*cohomology**theory*for Hausdorff gaps. ... In a future paper, we will examine the case*of*ω 1 -*trees*and develop a*cohomology**theory*for a class*of*Aronszajn*trees*. ...##
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Master index of volumes 51–60

1994
*
Topology and its Applications
*

ELSEVIER Topology and its

doi:10.1016/0166-8641(94)90010-8
fatcat:qluxdsirkbguvow77rovlp6bp4
*Applications*60 (1994) 297-304 Elsevier Science B.V. ... ., Completions*of*ranked spaces and their*applications**to*the study*of*nonabsolute integrals Nail, V.C., Partial confluence and closed subsets*of*a graph Nel, L.D., see Bonenfant, P. ... C.L., Determining topologies by collections*of*proper maps and by weak topologies Cortiiias, G., L-*theory*and dihedral homology*II*Katz, Equivariant semicharacteristics and induction Dqbski, ...##
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Page 904 of Mathematical Reviews Vol. , Issue 2000b
[page]

2000
*
Mathematical Reviews
*

branches

*of*the*tree*corresponding*to*the con- dition p’. ... The first derived limit lim”)*of**of*this inverse system is an object*of*interest in several areas*of*mathematics and has its origin in*cohomology**theory*. ...##
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The Cohomology of the Ordinals I: Basic Theory and Consistency Results
[article]

2019
*
arXiv
*
pre-print

This discussion occupies the first half

arXiv:1902.02736v2
fatcat:anqluhzlpjbazk35vxvdq3leyy
*of*our paper and is written with a general mathematical audience in mind. We turn in the paper's second half*to*more properly*set*-theoretic considerations. ... We show in particular that the Čech*cohomology*groups*of*the ordinals articulate higher-dimensional generalizations*of*Todorcevic's walks and coherent sequences techniques, and begin*to*account for those ... Portions*of*this material appeared in the first author's Ph.D. thesis; he would like*to*thank the members*of*his committee -Justin Moore, Slawomir Solecki, and Jim West -as well as Stevo*Todorcevic*, for ...##
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The first omega alephs: from simplices to trees of trees to higher walks
[article]

2021
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arXiv
*
pre-print

The point

arXiv:2008.03386v2
fatcat:z352uqtqi5f2hnllweqz4obege
*of*departure for the present work is Barry Mitchell's 1972 theorem that the*cohomological*dimension*of*ℵ_n is n+1. ...*sets*, nontrivial n-coherent families*of*functions, and higher-dimensional generalizations*of*portions*of*Todorcevic's walks technique. ... The periodic stimulus*of*conversations with Stevo*Todorcevic*has also richly informed this work. ...##
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Open problems in topology

2004
*
Topology and its Applications
*

In the notes

doi:10.1016/s0166-8641(03)00183-4
fatcat:hx5owowk25ftxducz667cxupiu
*to*this problem, Dow conjectured that there is a model satisfying that if X is compact and ω × X has remote points then X has an open subset with countable cellularity. ... Kunen [15] proved that if κ is a regular cardinal, then there is a weak P κ + -point in U(κ), the space*of*uniform ultrafilters on κ. Problem 5 only asked for the case κ = ω 1 . ... Also,*Tree*gave a ZFC example*of*a nonmetrizable pseudonormal Moore manifold (which is listed as a subproblem*to*Problem 314). Reed would like*to*note that P. ...##
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Problems from Topology Proceedings
[article]

2003
*
arXiv
*
pre-print

Arhangelskii's Structure and classification

arXiv:math/0312456v1
fatcat:g5aorxz3z5btlbxoawere25mdy
*of*topological spaces and cardinal invariants (1978); Continuum*theory*problems by Wayne Lewis (1983); Problems in continuum*theory*by Janusz R. ... 's that have some connection*to*the journal. ... These ideas may have*application*again in continua*theory*. Here is another*application**to*the zero-dimensional case. ...##
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Complete normality and metrization theory of manifolds

2002
*
Topology and its Applications
*

A space is collectionwise Hausdorff (cwH) if every closed discrete subspace D can be expanded

doi:10.1016/s0166-8641(01)00181-x
fatcat:76ku26s6grg2hgzpw6hpub6pwq
*to*a disjoint collection*of*open*sets*each*of*which meets D in one point. ... A manifold is a connected Hausdorff space in which every point has a neighborhood homeomorphic*to*Euclidean n-space (n is unique). ... Then, in 1978, Rudin showed that the existence*of*perfectly normal nonmetrizable manifolds was independent*of*the usual axioms*of**set**theory*[6] , by showing that they do not exist under MA(ω 1 ). ...##
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Structurable equivalence relations

2018
*
Fundamenta Mathematicae
*

For a class K

doi:10.4064/fm428-7-2017
fatcat:3wv3gcyaq5gupp7v5yw3464emq
*of*countable relational structures, a countable Borel equivalence relation E is said*to*be K-structurable if there is a Borel way*to*put a structure in K on each E-equivalence class. ... Finally, we consider the effect on K-structurability*of*various model-theoretic properties*of*K. ... Kechris-Solecki-*Todorcevic*[KST, 7 .1] proved a universality result for*theories**of*graphs, which was then extended*to*arbitrary*theories*by Miller; see Corollary 4.4. ...##
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Structurable equivalence relations
[article]

2018
*
arXiv
*
pre-print

For a class K

arXiv:1606.01995v5
fatcat:b5qy5eim4fgp5jjcplmepwgrgi
*of*countable relational structures, a countable Borel equivalence relation E is said*to*be K-structurable if there is a Borel way*to*put a structure in K on each E-equivalence class. ... Finally, we consider the effect on K-structurability*of*various model-theoretic properties*of*K. ... We are also grateful*to*Anush Tserunyan for extensive comments and suggestions, including spotting and correcting an error in the original version*of*Lemma 8.3. ...##
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Dimensions of ordinals: set theory, homology theory, and the first omega alephs

2018

Some

doi:10.7298/x4w37tkk
fatcat:r2bivg24rfgr3dlnfiwygqsvaq
*of*their contributions will grow plainer in the pages below. The organizing and overarching intellectual debt is very obviously*to*the works*of*Stevo*Todorcevic*and Sibe Mardešić. ... Fundamental*to*all my thinking, finally, are three teachers each*of*whom is*of*a sort that one finds, with luck, maybe once in a lifetime. ... The standing kindnesses*of*parents come in many ways first, and condition all the rest. ...##
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Sites whose topoi are the smooth representations of locally profinite groups
[article]

2017
*
arXiv
*
pre-print

We define a class

arXiv:1506.08023v2
fatcat:c2o4krhudbcjffsraxc3eauyrm
*of*sites such that the associated topos is equivalent*to*the category*of*smooth*sets*(representations)*of*some locally prodiscrete monoids (*to*be defined). ... We then define a subclass*of*sites such that the topos is equivalent*to*the category*of*discrete*sets*with a continuous action*of*a locally profinite group. ... We took the term 'smooth' from the representation*theory**of*locally profinite groups, which is known for its*applications*in number*theory*(see Remark 5.7.8) . ...