Friedman, Sy D. 1953
Overview
Works:  13 works in 41 publications in 1 language and 663 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA9.7, 511.322 
Publication Timeline
.
Most widely held works by
Sy D Friedman
Fine structure and class forcing by
Sy D Friedman(
Book
)
15 editions published between 2000 and 2011 in English and held by 143 WorldCat member libraries worldwide
15 editions published between 2000 and 2011 in English and held by 143 WorldCat member libraries worldwide
Generalized descriptive set theory and classification theory by
Sy D Friedman(
Book
)
11 editions published between 2013 and 2014 in English and held by 108 WorldCat member libraries worldwide
Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of firstorder theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations
11 editions published between 2013 and 2014 in English and held by 108 WorldCat member libraries worldwide
Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of firstorder theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations
Logic Colloquium '01 : proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, held in Vienna,
Austria, August 611, 2001 by
Wien) Logic Colloquium (2001(
Book
)
5 editions published in 2005 in English and held by 62 WorldCat member libraries worldwide
5 editions published in 2005 in English and held by 62 WorldCat member libraries worldwide
Recursion on inadmissible ordinals by
Sy D Friedman(
Book
)
1 edition published in 1976 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1976 in English and held by 2 WorldCat member libraries worldwide
Ordinal recursion theory by
C.T Chong(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Forcing with finite conditions by
Sy D Friedman(
Book
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Measurable cardinals and the cofinality of the symmetric group by
Sy D Friedman(
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Assuming the existence of a $P_2\kappa$hypermeasurable cardinal, we construct a model of set theory with a measurable cardinal $\kappa$ such that $2^\kappa=\kappa^{++}$ and the group $\text{Sym}(\kappa)$ of all permutations of $\kappa$ cannot be written as the union of a chain of proper subgroups of length $<\kappa^{++}$. The proof involves iteration of a suitably defined uncountable version of the Miller forcing poset as well as the "tuning fork" argument introduced by the first author and K.Thompson [J. Symb. Log. 73, No. 3, 906918 (2008)]
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Assuming the existence of a $P_2\kappa$hypermeasurable cardinal, we construct a model of set theory with a measurable cardinal $\kappa$ such that $2^\kappa=\kappa^{++}$ and the group $\text{Sym}(\kappa)$ of all permutations of $\kappa$ cannot be written as the union of a chain of proper subgroups of length $<\kappa^{++}$. The proof involves iteration of a suitably defined uncountable version of the Miller forcing poset as well as the "tuning fork" argument introduced by the first author and K.Thompson [J. Symb. Log. 73, No. 3, 906918 (2008)]
Cardinal characteristics, projective wellorders and large continuum by Vera Fischer(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We extend the work of Fischer et al. (2011) [Projective wellorders and mad families with large continuum, Ann. Pure Appl. Logic, 162 (2011), pp. 853862] by presenting a method for controlling cardinal characteristics in the presence of a projective wellorder and $2^{\aleph_0} > \aleph_2$. This also answers a question of Harrington (1977) [Long projective wellorderings Ann. Math. Logic, 12 (1977), pp. 124] by showing that the existence of a $\Delta^1_3$ wellorder of the reals is consistent with Martin's axiom and $2^{\aleph_0} > \aleph_3$
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We extend the work of Fischer et al. (2011) [Projective wellorders and mad families with large continuum, Ann. Pure Appl. Logic, 162 (2011), pp. 853862] by presenting a method for controlling cardinal characteristics in the presence of a projective wellorder and $2^{\aleph_0} > \aleph_2$. This also answers a question of Harrington (1977) [Long projective wellorderings Ann. Math. Logic, 12 (1977), pp. 124] by showing that the existence of a $\Delta^1_3$ wellorder of the reals is consistent with Martin's axiom and $2^{\aleph_0} > \aleph_3$
Projective wellorders and mad families with large continuum by Vera Fischer(
)
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
We show that $\mathfrak b = \mathfrak c = \omega _3$ is consistent with the existence of a $\Delta_3^1$definable wellorder of the reals and a $\Pi_2^1$definable $\omega$mad subfamily of $[\omega ]^\omega$ (resp. $\omega ^\omega$)
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
We show that $\mathfrak b = \mathfrak c = \omega _3$ is consistent with the existence of a $\Delta_3^1$definable wellorder of the reals and a $\Pi_2^1$definable $\omega$mad subfamily of $[\omega ]^\omega$ (resp. $\omega ^\omega$)
Fusion and large cardinal preservation by
Sy D Friedman(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
In this paper we introduce some fusion properties of forcing notions which guarantee that an iteration with supports of size $\le \kappa$ not only does not collapse $\kappa^+$ but also preserves the strength of $\kappa$ (after a suitable preparatory forcing). This provides a general theory covering the known cases of tree iterations which preserve large cardinals
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
In this paper we introduce some fusion properties of forcing notions which guarantee that an iteration with supports of size $\le \kappa$ not only does not collapse $\kappa^+$ but also preserves the strength of $\kappa$ (after a suitable preparatory forcing). This provides a general theory covering the known cases of tree iterations which preserve large cardinals
Fusion and large cardinals by Lyubomyr Zdomskyy(
)
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
Projective mad families by
Sy D Friedman(
)
1 edition published in 2010 in English and held by 0 WorldCat member libraries worldwide
Using almost disjoint coding we prove the consistency of the existence of a $\Pi_2^1$definable $\omega$mad family of infinite subsets of $\omega$ (resp. functions from $\omega$ to $\omega$) together with $\mathfrak{b} = 2^\omega = \omega_2$
1 edition published in 2010 in English and held by 0 WorldCat member libraries worldwide
Using almost disjoint coding we prove the consistency of the existence of a $\Pi_2^1$definable $\omega$mad family of infinite subsets of $\omega$ (resp. functions from $\omega$ to $\omega$) together with $\mathfrak{b} = 2^\omega = \omega_2$
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Related Identities
 Hyttinen, Tapani
 Kulikov, Vadim 1986
 Baaz, Matthias Editor
 Krajíček, Jan Editor
 American Mathematical Society
 ebrary, Inc
 Zdomskyy, Lyubomyr Author
 Honzík, Radek
 Fischer, Vera Author
 Chong, C. T. Author
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Alternative Names
Friedman, S.D.
Friedman, Sy D.
Friedman, Sy D. 1953
Friedman, SyDavid.
Friedman, SyDavid 1953
Sy Friedman American mathematician
Sy Friedman amerikansk matematikar
Sy Friedman amerikansk matematiker
Sy Friedman USamerikanischer Mathematiker
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