On a partition calculus of partial orders

Mátrai Tamás Highland Park

Informations

• Publié par: Sonab
• Nombre de lectures: 33
• Langue: English

Extrait

On a partition calculus of
partial orders
Tam as atraiM
Alfred Renyi Institute
Starkville
March 20, 2010
www.renyi.hu/ matraiton
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The purpose
theory of co nal similarity types;
Tukey reductions: Moore-Smith convergence;
topological aspects of the theory;
combinatorial aspects of the theory.p
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co nally similar: R; u.d.p.o. set,
P;Q R into co nal subsets
Tukey reducible: P Q if g : Q P,T
g maps co nal subsets to co nal subsets
Easy observations:
P, Q are co nally similar if and only if P Q, i.e.T
P Q and Q PT T
P Q if and only if f : P Q,T
f maps unbounded subsets to unbounded subsets
Co nal types
P; , Q; upward directed partially ordered setsp
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Tukey reducible: P Q if g : Q P,T
g maps co nal subsets to co nal subsets
Easy observations:
P, Q are co nally similar if and only if P Q, i.e.T
P Q and Q PT T
P Q if and only if f : P Q,T
f maps unbounded subsets to unbounded subsets
Co nal types
P; , Q; upward directed partially ordered sets
co nally similar: R; u.d.p.o. set,
P;Q R into co nal subsetsÑ
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Easy observations:
P, Q are co nally similar if and only if P Q, i.e.T
P Q and Q PT T
P Q if and only if f : P Q,T
f maps unbounded subsets to unbounded subsets
Co nal types
P; , Q; upward directed partially ordered sets
co nally similar: R; u.d.p.o. set,
P;Q R into co nal subsets
Tukey reducible: P Q if g : Q P,T
g maps co nal subsets to co nal subsetsp
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P Q if and only if f : P Q,T
f maps unbounded subsets to unbounded subsets
Co nal types
P; , Q; upward directed partially ordered sets
co nally similar: R; u.d.p.o. set,
P;Q R into co nal subsets
Tukey reducible: P Q if g : Q P,T
g maps co nal subsets to co nal subsets
Easy observations:
P, Q are co nally similar if and only if P Q, i.e.T
P Q and Q PT Tp
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Co nal types
P; , Q; upward directed partially ordered sets
co nally similar: R; u.d.p.o. set,
P;Q R into co nal subsets
Tukey reducible: P Q if g : Q P,T
g maps co nal subsets to co nal subsets
Easy observations:
P, Q are co nally similar if and only if P Q, i.e.T
P Q and Q PT T
P Q if and only if f : P Q,T
f maps unbounded subsets to unbounded subsetsp
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T. Bartosynski: Tukey reductions account for all inequalities
in the Cichon diagram;
S. Todorcevic: co nal types of d.p.o. sets of cardinality ! is1
unclassi able in ZFC;
D. Fremlin: the Maharam type of a (. . . ) measure space
X; is determined by the co nal type of N ; ;X;
D. Fremlin: a characterization of some topological properties
of X in terms of the co nal type of K X ; ;
analytic ideals: I P ! such that I is analytic, ideal;
The historyp
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S. Todorcevic: co nal types of d.p.o. sets of cardinality ! is1
unclassi able in ZFC;
D. Fremlin: the Maharam type of a (. . . ) measure space
X; is determined by the co nal type of N ; ;X;
D. Fremlin: a characterization of some topological properties
of X in terms of the co nal type of K X ; ;
analytic ideals: I P ! such that I is analytic, ideal;
The history
T. Bartosynski: Tukey reductions account for all inequalities
in the Cichon diagram;:
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lo
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p
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D. Fremlin: the Maharam type of a (. . . ) measure space
X; is determined by the co nal type of N ; ;X;
D. Fremlin: a characterization of some topological properties
of X in terms of the co nal type of K X ; ;
analytic ideals: I P ! such that I is analytic, ideal;
The history
T. Bartosynski: Tukey reductions account for all inequalities
in the Cichon diagram;
S. Todorcevic: co nal types of d.p.o. sets of cardinality ! is1
unclassi able in ZFC;