A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
The generalized Kurepa hypothesis at singular cardinals
[article]

2020
*
arXiv
*
pre-print

We discuss

arXiv:1712.02487v2
fatcat:fruhjmqvi5da7aevxmg5iro2wy
*the**generalized**Kurepa**hypothesis*KH_λ at singular cardinals λ. ... In particular, we answer questions of Erdös-Hajnal [1] and Todorcevic [6], [7] by showing that GCH does not imply KH_ℵ_ω nor*the*existence of a family F⊆ [ℵ_ω]^ℵ_0 of size ℵ_ω+1 such that F X has size ... introduction For an infinite cardinal λ let*the**generalized**Kurepa**hypothesis*at λ, denoted KH λ , be*the*assertion: there exists a family F ⊆ P (λ) such that |F | > λ but |F ↾ X| ≤ |X| for every infinite ...##
###
A theorem on the closure of Ω-pure subgroups of CΩ groups in the Ω-topology

1989
*
Journal of Algebra
*

If we assume

doi:10.1016/0021-8693(89)90298-6
fatcat:3sj2t3iecraunbvzq37fx23yme
*the*continuum*hypothesis*(2%= H,), we can exhibit a specific example of a group which is close to being a dsc, but fails to be a dsc as follows: By [RW] there. is a balanced subgroup of a ... As was pointed out in*the*proof of Theorem 15, if we define Tar(G) = G. Theorems 15 and 17 are valid when n = 1. ...*The*main*result*of [K3] is that*the*existence of K-*Kurepa*subgroups is equivalent to*the*existence of families of sets of cardinality K satisfying Kurepa's*Hypothesis*(KH) . ...##
###
Page 436 of Mathematical Reviews Vol. 34, Issue 3
[page]

1967
*
Mathematical Reviews
*

Throughout most of our work we assume

*the**general*continuum*hypothesis*. “In § 17 we prove a negative*result**on*II-relations which is sharper than that obtained by Erdés and Hajnal [Acta Math. Acad. ... Independently of Erdés and Rado and at about*the*same time,*Kurepa*found several I- relations,*the*most important of which, deduced under*the*assumption of*the**generalized*continuum*hypothesis*, can be ...##
###
Page 5795 of Mathematical Reviews Vol. , Issue 91K
[page]

1991
*
Mathematical Reviews
*

Hugh (1-CA)

*The**generalized*continuum*hypothesis*can fail everywhere. Ann. of Math. (2) 133 (1991), no. 1, 1-35. ...*The*subject matter need not be a unique, Platonic realm. This kind of*generality*is taken as*one*of*the*two essential and defining principles. ...##
###
Book Review: Aspects of constructibility

1975
*
Bulletin of the American Mathematical Society
*

Besides, L satisfies

doi:10.1090/s0002-9904-1975-13860-2
fatcat:avigu72rjndfflrxfshjdcu7qe
*the**generalized*continuum*hypothesis*, i.e. 2 Xot =N a +i for every infinite cardinal K«. ... (That includes Souslin Problem,*Kurepa**Hypothesis*, different partition problems, two cardinals problems in model theory, etc.) ...*The*proof of*Kurepa**Hypothesis*in L again extracts*the*right combinatorial property (0 + in this case). ...##
###
On Kurepa's problems in number Theory
[article]

2003
*
arXiv
*
pre-print

We discuss some problems in number theory posed by Djuro

arXiv:math/0312202v1
fatcat:xzxejlagerb23hm72lbc6jizze
*Kurepa*(1907-1993), including his classical left factorial*hypothesis*that an odd prime p does not divide 0! + 1! + ... + (p-1)!. ... This conjecture, known as*the*left factorial*hypothesis*, is still an open problem in number theory. There are several*results*which support*the*truth of*the**hypothesis*. ... Further*results**on*K(z) as a function of*the*complex variable z were obtained by Slavić [Sl] . His main*result*is that K(z) = − π e cotgπz + 1 e ∞ k=1 1 n! ...##
###
On the History of Souslin's Problem

1999
*
Archive for History of Exact Sciences
*

*Kurepa*1935, p. 109. 85 "According to

*the*

*results*given in

*the*last paragraphs,

*the*

*hypothesis*that every ramified table of power ℵ 1 is normal (or, equivalently, that every distinguished sequence of ... there is an F-

*generic*filter

*on*P . ...

##
###
Automorphisms of $\omega \sb{1}$-trees

1972
*
Transactions of the American Mathematical Society
*

.); by

doi:10.1090/s0002-9947-1972-0347605-1
fatcat:dwiazgmy4ve6lckq73lnyxswwe
*the*induction*hypothesis*, T |aDT|a. We consider three cases. Case I. For some ß, a. = ß + 1. ... Here we*generalize*this*result*to show, by*the*way of consistency, that o(T) can be anything it is allowed to be. First we prove a refinement of Theorem 1 to show what o(T) is allowed to be. ... without proving*the*existence of a rigid tree. We conclude with*the*following problem; we are inclined rather to believe in*the*negative solution: Problem. ...##
###
Partitioning pairs of countable sets

1991
*
Proceedings of the American Mathematical Society
*

We make

doi:10.1090/s0002-9939-1991-1036992-4
fatcat:35lhydg26vea7jl5jyfkdhvl74
*the*translations of our partitions from [3] in*the*context of all countable subsets of a fixed uncountable set. A different translation was obtained recently by Velleman [4] . ...*The*proof will use straightforward*generalization*of*one*of*the*partitions from [3] . ... Since*the*family of singletons of elements of A is clearly a*Kurepa*family in [A] °,*the**hypothesis*of*the*second theorem is satisfied when*the*stationary cofinality of [A]*0 is equal to*the*size of A ...##
###
Partitioning Pairs of Countable Sets

1991
*
Proceedings of the American Mathematical Society
*

We make

doi:10.2307/2048422
fatcat:tjryqm2xerb2xbebxumld67iw4
*the*translations of our partitions from [3] in*the*context of all countable subsets of a fixed uncountable set. A different translation was obtained recently by Velleman [4] . ...*The*proof will use straightforward*generalization*of*one*of*the*partitions from [3] . ... Since*the*family of singletons of elements of A is clearly a*Kurepa*family in [A] °,*the**hypothesis*of*the*second theorem is satisfied when*the*stationary cofinality of [A]*0 is equal to*the*size of A ...##
###
Page 575 of Mathematical Reviews Vol. 24, Issue 6A
[page]

1962
*
Mathematical Reviews
*

For p, q, tr, and 8 infinite,

*the*authors give a complete answer based*on**the**generalized*continuum*hypothesis*, and a partial answer without this*hypothesis*. ...*The*pre- sentation, which is sketchy, consists in listing of*results*and problems with hints to references. D.*Kurepa*(Zagreb) A3073 Cuesta, N. Mathematical*generators*. ...##
###
Page 1763 of Mathematical Reviews Vol. 51, Issue 6
[page]

1976
*
Mathematical Reviews
*

*hypothesis*is equivalent to weak compactness, and a generalised

*Kurepa*

*hypothesis*is equivalent to ineffability (a notion first found in this context). ... Logic 4 (1972), 229-308; erratum, ibid. 4 (1972), 443; MR 46 #8834], and

*the*generalisations of

*the*

*results*

*on*Suslin and

*Kurepa*hypotheses to higher cardinals follow; thus if V=L, a generalised Suslin ...

##
###
Descriptive properties of higher Kurepa trees
[article]

2021
*
arXiv
*
pre-print

We use

arXiv:2010.11597v2
fatcat:oxxrsdvmlzdunicg62vh7w3b4q
*generalizations*of concepts from descriptive set theory to study combinatorial objects of uncountable regular cardinality, focussing*on*higher*Kurepa*trees and*the*representation of*the*sets of ... of*the**generalized*Baire space ^κκ of κ. ...*The*proof of*the*following theorem relies*on*a*result*of Donder*on**the*structural properties of*the**Kurepa*trees constructed from*the*canonical morasses at successor cardinals in*the*constructible universe ...##
###
Kurepa trees and spectra of L_ω_1,ω-sentences
[article]

2018
*
arXiv
*
pre-print

We construct a single L_ω_1,ω-sentence ψ that codes

arXiv:1705.05821v2
fatcat:pyyv6oiw5jf5jog3ld6xj4gxje
*Kurepa*trees to prove*the*consistency of*the*following: (1)*The*spectrum of ψ is consistently equal to [_0,_ω_1] and also consistently equal to [_0,2 ... Our*result*proves that 2^_0 can not be replaced by 2^_1, even if 2^_0<_ω_1. ...*The*ideas of Lemma 2.2 and Theorem 3.7 were communicated to*the*authors by Philipp Lücke.*The*consistency*results*of Section 3 were based*on*early ideas of Stevo Todorcevic. ...##
###
Page 1780 of Mathematical Reviews Vol. , Issue 92d
[page]

1992
*
Mathematical Reviews
*

*The*

*generic*

*Kurepa*

*hypothesis*(GKH) asserts that a

*Kurepa*tree may be adjoined to

*the*universe by ccc forcing. ... {See also

*the*preceding review. } Dag Normann (N-OSLO) 92d:03037 03E35 03E45 03E55 Jensen, R. B. (4-OXAS); Schlechta, K. (D-IBM3)

*Results*

*on*

*the*

*generic*

*Kurepa*

*hypothesis*. Arch. Math. ...

« Previous

*Showing results 1 — 15 out of 619 results*