Descriptive Set Theory and Forcing
How to prove theorems about Borel sets the hard way
(Sprache: Englisch)
This advanced graduate course assumes some knowledge of forcing as well as some elementary mathematical logic, e.g. the Lowenheim-Skolem Theorem. The first half deals with the general area of Borel hierarchies, probing lines of enquiry such as the possible...
Leider schon ausverkauft
versandkostenfrei
Buch (Kartoniert)
93.99 €
46 DeutschlandCard Punkte
sammeln
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenlose Rücksendung
- Ratenzahlung möglich
Produktdetails
Produktinformationen zu „Descriptive Set Theory and Forcing “
Klappentext zu „Descriptive Set Theory and Forcing “
This advanced graduate course assumes some knowledge of forcing as well as some elementary mathematical logic, e.g. the Lowenheim-Skolem Theorem. The first half deals with the general area of Borel hierarchies, probing lines of enquiry such as the possible lengths of a Borel hierarchy in a separable metric space. The second half goes on to include Harrington's Theorem together with a proof and applications of Louveau's Theorem on hyperprojective parameters.
Inhaltsverzeichnis zu „Descriptive Set Theory and Forcing “
1 What are the reals, anyway?I On the length of Borel hierarchies
2 Borel Hierarchy
3 Abstract Borel hierarchies
4 Characteristic function of a sequence
5 Martin's Axiom
6 Generic G?
7 ?-forcing
8 Boolean algebras
9 Borel order of a field of sets
10 CH and orders of separable metric spaces
11 Martin-Solovay Theorem
12 Boolean algebra of order ?1
13 Luzin sets
14 Cohen real model
15 The random real model
16 Covering number of an ideal
II Analytic sets
17 Analytic sets
18 Constructible well-orderings
19 Hereditarily countable sets
20 Shoenfield Absoluteness
21 Mansfield-Solovay Theorem
22 Uniformity and Scales
23 Martin's axiom and Constructibility
- 24
% MathType!MTEF!2!1!+-
% feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm
% Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHris5daqhaaWcbaGaeGOmaidabaGaeG
% ymaedaaaaa!3322!
$$
\sum _2^1
$$ well-orderings
25 Large
% MathType!MTEF!2!1!+-
% feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm
% Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHpis1daqhaaWcbaGaeGOmaidabaGaeG
% ymaedaaaaa!3310!
$$
\prod _2^1
$$ sets
III Classical Separation Theorems
26 Souslin-Luzin Separation Theorem
27 Kleene Separation Theorem
- 28
% MathType!MTEF!2!1!+-
% feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm
% Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHpis1daqhaaWcbaGaeGymaedabaGaeG
% ymaedaaaaa!330E!
$$
\prod _1^1
$$-Reduction
- 29
% MathType!MTEF!2!1!+-
% feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm
%
... mehr
Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHuoardaqhaaWcbaGaeGymaedabaGaeG
% ymaedaaaaa!32E3!
$$
\Delta _1^1
$$-codes
IV Gandy Forcing
- 30
% MathType!MTEF!2!1!+-
% feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm
% Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHpis1daqhaaWcbaGaeGymaedabaGaeG
% ymaedaaaaa!330E!
$$
\prod _1^1
$$ equivalence relations
31 Borel metric spaces and lines in the plane
- 32
% MathType!MTEF!2!1!+-
% feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm
% Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHris5daqhaaWcbaGaeGymaedabaGaeG
% ymaedaaaaa!3320!
$$
\sum _1^1
$$ equivalence relations
33 Louveau's Theorem
34 Proof of Louveau's Theorem
- References
- Elephant Sandwiches
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHuoardaqhaaWcbaGaeGymaedabaGaeG
% ymaedaaaaa!32E3!
$$
\Delta _1^1
$$-codes
IV Gandy Forcing
- 30
% MathType!MTEF!2!1!+-
% feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm
% Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHpis1daqhaaWcbaGaeGymaedabaGaeG
% ymaedaaaaa!330E!
$$
\prod _1^1
$$ equivalence relations
31 Borel metric spaces and lines in the plane
- 32
% MathType!MTEF!2!1!+-
% feaagCart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm
% Wu51MyVXgaruWqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9
% q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir
% -Jbba9q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGa
% aeqabaWaaeaaeaaakeaacqGHris5daqhaaWcbaGaeGymaedabaGaeG
% ymaedaaaaa!3320!
$$
\sum _1^1
$$ equivalence relations
33 Louveau's Theorem
34 Proof of Louveau's Theorem
- References
- Elephant Sandwiches
... weniger
Bibliographische Angaben
- Autor: Arnold Miller
- 1995, 1995., 133 Seiten, Maße: 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540600590
- ISBN-13: 9783540600596
Sprache:
Englisch
Rezension zu „Descriptive Set Theory and Forcing “
"Miller includes interesting historical material and references. His taste for slick, elegant proofs makes the book pleasant to read. The author makes good use of his sense of humor...Most readers will enjoy the comments, footnotes, and jokes scattered throughout the book." Studia Logica
Kommentar zu "Descriptive Set Theory and Forcing"
0 Gebrauchte Artikel zu „Descriptive Set Theory and Forcing“
| Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
|---|
Schreiben Sie einen Kommentar zu "Descriptive Set Theory and Forcing".
Kommentar verfassen