scholarly journals Perfect set of Euler tours of K_{p,p,p}

2016 ◽  
Vol 36 (4) ◽  
pp. 783
Author(s):  
Thamodharan Govindan ◽  
Appu Muthusamy
Keyword(s):  
Perfect Set ◽  
Euler Tours

A COMBINATORIAL CORE OF THE ITERATED PERFECT SET MODEL

1999 ◽  
Vol 25 (1) ◽  
pp. 137
Author(s):  
Ciesielski
Keyword(s):  
Perfect Set

Random Sampling of Euler Tours

Algorithmica ◽  
2001 ◽  
Vol 30 (3) ◽  
pp. 376-385 ◽  
Author(s):  
P. Tetali ◽  
S. Vempala
Keyword(s):  
Random Sampling ◽  
Euler Tours

Constructible lattices of c-degrees

1982 ◽  
Vol 47 (4) ◽  
pp. 739-754
Author(s):  
C.P. Farrington
Keyword(s):  
Set Theory ◽  
Regular Cardinal ◽  
Boolean Algebras ◽  
Combinatorial Complexity ◽  
Generic Extension ◽  
Transitive Model ◽  
Perfect Set ◽  
Consistency Results ◽  
Combinatorial Principles ◽  
Souslin Trees

This paper is devoted to the proof of the following theorem.Theorem. Let M be a countable standard transitive model of ZF + V = L, and let ℒ Є M be a wellfounded lattice in M, with top and bottom. Let ∣ℒ∣M = λ, and suppose κ ≥ λ is a regular cardinal in M. Then there is a generic extension N of M such that(i) N and M have the same cardinals, and κN ⊂ M;(ii) the c-degrees of sets of ordinals of N form a pattern isomorphic to ℒ;(iii) if A ⊂ On and A Є N, there is B Є P(κ+)N such that L(A) = L(B).The proof proceeds by forcing with Souslin trees, and relies heavily on techniques developed by Jech. In [5] he uses these techniques to construct simple Boolean algebras in L, and in [6] he uses them to construct a model of set theory whose c-degrees have orderlype 1 + ω*.The proof also draws on ideas of Adamovicz. In [1]–[3] she obtains consistency results concerning the possible patterns of c-degrees of sets of ordinals using perfect set forcing and symmetric models. These methods have the advantage of yielding real degrees, but involve greater combinatorial complexity, in particular the use of ‘sequential representations’ of lattices.The advantage of the approach using Souslin trees is twofold: first, we can make use of ready-made combinatorial principles which hold in L, and secondly, the notion of genericity over a Souslin tree is particularly simple.

scholarly journals Review of Locke’s Metaphysics by Matthew Stuart

Locke Studies ◽  
2014 ◽  
Vol 14 ◽  
pp. 263-271
Author(s):  
Victor Nuovo
Keyword(s):  
Perfect Set ◽  
Navigational Aids

This is a substantial book in several ways. To begin with, it is great in bulk and long in content. But it is so well ordered that in spite of its length it can be navigated with ease. Its contents are topically arranged. Its seventy sections numbered consecutively are distributed among ten chapters. Its topics and subtopics are described in a table of contents and elaborated in summaries at the head of each chapter, which provide the reader with a running argument. With these aids, it is possible to survey the entire contents of the book in short order and to jump from one place to another without losing one’s way. A table of contents and index locorum complete a perfect set of navigational aids. The method is reminiscent of Locke.

Small Coverings with Smooth Functions under the Covering Property Axiom

2005 ◽  
Vol 57 (3) ◽  
pp. 471-493 ◽  
Author(s):  
Krzysztof Ciesielski ◽  
Janusz Pawlikowski
Keyword(s):  
Borel Function ◽  
Covering Property ◽  
Smooth Functions ◽  
Differentiable Functions ◽  
Perfect Set ◽  
Covering Property Axiom

AbstractIn the paper we formulate a Covering Property Axiom, CPAprism, which holds in the iterated perfect set model, and show that it implies the following facts, of which (a) and (b) are the generalizations of results of J. Steprāns.(a) There exists a family ℱ of less than continuummany functions from ℝ to ℝ such that ℝ2 is covered by functions from ℱ, in the sense that for every 〈x, y〉 ∈ ℝ2 there exists an f ∈ ℱ such that either f (x) = y or f (y) = x.(b) For every Borel function f : ℝ → ℝ there exists a family ℱ of less than continuum many “” functions (i.e., differentiable functions with continuous derivatives, where derivative can be infinite) whose graphs cover the graph of f.(c) For every n > 0 and a Dn function f: ℝ → ℝ there exists a family ℱ of less than continuum many Cn functions whose graphs cover the graph of f.We also provide the examples showing that in the above properties the smoothness conditions are the best possible. Parts (b), (c), and the examples are closely related to work of A. Olevskiĭ.

Sign in / Sign up

Export Citation Format

Share Document