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  • 1
    Electronic Resource
    Electronic Resource
    Topological Partition Relations of the Form ω*→(Y)12 (1993)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 704 (1993), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Notes: . THEOREM. The topological partition relation ω*→ (Y)12(a) Fails for every space Y with |Y| |Mg 2c;(b) Holds for Y discrete if and only if |Y| |Ml c;(c) Holds for certain nondiscrete P-spaces Y;(d) Fails for Y=ω Imu {p} with p∉ω*;(e) Fails for Y infinite and countably compact.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1993.tb52510.x
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  • 2
    Electronic Resource
    Electronic Resource
    Lawless order (1985)
    Springer
    Order 1 (1985), S. 383-397 
    Details
    ISSN: 1572-9273
    Keywords: Primary 06F15, 06A05 ; secondary 03E99 ; Ordered groups ; varieties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract R. Baer asked whether the group operation of every (totally) ordered group can be redefined, keeping the same ordered set, so that the resulting structure is an Abelian ordered group. The answer is no. We construct an ordered set (G, ⩽) which carries an ordered group (G, •, ⩽) but which islawless in the following sense. If (G, *, ⩽) is an ordered group on the same carrier (G, ⩽), then the group (G, *) satisfies no nontrivial equational law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00582744
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  • 3
    Electronic Resource
    Electronic Resource
    $$L_{\infty _\omega }$$ free algebras (1989)
    Springer
    Algebra universalis 26 (1989), S. 351-366 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the study of which varieties, in a countable similarity type, have non-free $$L_{\infty _\omega }$$ (or equivalently ℵ1-free) algebras is completed. It was previously known that if a variety satisfies a property known as the construction principle then there are such algebras. If a variety does not satisfy the construction principle then either every $$L_{\infty _\omega }$$ -free algebra is free or for every infinite cardinalk, there is a k+-free algebra of cardinality k+ which is not free. Under the set theoretic assumption V=L, for any varietyV in a countable similarity type, either the class of free algebras is definable in $$L_{\omega _1 \omega }$$ or it is not definable in any $$L_{\infty _\kappa }$$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211842
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  • 4
    Electronic Resource
    Electronic Resource
    The structure of ext (A,ℤ) andV=L (1978)
    Springer
    Mathematische Zeitschrift 162 (1978), S. 39-50 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01437821
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  • 5
    Electronic Resource
    Electronic Resource
    Modules over arbitrary domains (1985)
    Springer
    Mathematische Zeitschrift 188 (1985), S. 325-337 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01159179
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  • 6
    Electronic Resource
    Electronic Resource
    On certain indestructibility of strong cardinals and a question of Hajnal (1989)
    Springer
    Archive for mathematical logic 28 (1989), S. 35-42 
    Details
    ISSN: 1432-0665
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A model in which strongness ofκ is indestructible under κ+ -weakly closed forcing notions satisfying the Prikry condition is constructed. This is applied to solve a question of Hajnal on the number of elements of {λ δ |2 δ 〈λ}.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01624081
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  • 7
    Electronic Resource
    Electronic Resource
    Reflecting stationary sets and successors of singular cardinals (1991)
    Springer
    Archive for mathematical logic 31 (1991), S. 25-53 
    Details
    ISSN: 1432-0665
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract REF is the statement that every stationary subset of a cardinal reflects, unless it fails to do so for a trivial reason. The main theorem, presented in Sect. 0, is that under suitable assumptions it is consistent that REF and there is a κ which is κ+n -supercompact. The main concepts defined in Sect. 1 are PT, which is a certain statement about the existence of transversals, and the “bad” stationary set. It is shown that supercompactness (and even the failure of PT) implies the existence of non-reflecting stationary sets. E.g., if REF then for manyλ ⌝ PT(λ, ℵ1). In Sect. 2 it is shown that Easton-support iteration of suitable Levy collapses yield a universe with REF if for every singular λ which is a limit of supercompacts the bad stationary set concentrates on the “right” cofinalities. In Sect. 3 the use of oracle c.c. (and oracle proper—see [Sh-b, Chap. IV] and [Sh 100, Sect. 4]) is adapted to replacing the diamond by the Laver diamond. Using this, a universe as needed in Sect. 2 is forced, where one starts, and ends, with a universe with a proper class of supercompacts. In Sect. 4 bad sets are handled in ZFC. For a regular λ {δ〈+ : cfδ〈λ} is good. It is proved in ZFC that ifλ=cfλ〉ℵ1 then {α〈+ : cfα〈λ} is the union of λ sets on which there are squares.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01370693
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  • 8
    Electronic Resource
    Electronic Resource
    Maximal chains inωω and ultrapowers of the integers (1993)
    Springer
    Archive for mathematical logic 32 (1993), S. 305-319 
    Details
    ISSN: 1432-0665
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Various questions posed by P. Nyikos concerning ultrafilters on ω and chains in the partial order (ω, 〈*) are answered. The main tool is the oracle chain condition and variations of it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01409965
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  • 9
    Electronic Resource
    Electronic Resource
    Erratum (1994)
    Springer
    Archive for mathematical logic 33 (1994), S. 167-168 
    Details
    ISSN: 1432-0665
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01352936
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  • 10
    Electronic Resource
    Electronic Resource
    More on cardinal arithmetic (1993)
    Springer
    Archive for mathematical logic 32 (1993), S. 399-428 
    Details
    ISSN: 1432-0665
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01270465
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