Rado's Conjecture and Ascent Paths of Square Sequences

2014 ◽  
Vol 60 (1-2) ◽  
pp. 84-90 ◽  
Author(s):  
Stevo Todorčević ◽  
Víctor Torres Pérez
Keyword(s):  
Square Sequences

scholarly journals Weak square sequences and special Aronszajn trees

2013 ◽  
Vol 221 (3) ◽  
pp. 267-284 ◽  
Author(s):  
John Krueger
Keyword(s):  
Aronszajn Trees ◽  
Square Sequences ◽  
Weak Square

scholarly journals Autocorrelation Values of Generalized Cyclotomic Sequences with Period pn+1

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 950
Author(s):  
Xiaolin Chen ◽  
Huaning Liu
Keyword(s):  
Positive Integer ◽  
Linear Complexity ◽  
Character Sums ◽  
Binary Sequences ◽  
Square Sequences ◽  
Cyclotomic Sequences

Recently Edemskiy proposed a method for computing the linear complexity of generalized cyclotomic binary sequences of period p n + 1 , where p = d R + 1 is an odd prime, d , R are two non-negative integers, and n > 0 is a positive integer. In this paper we determine the exact values of autocorrelation of these sequences of period p n + 1 ( n ≥ 0 ) with special subsets. The method is based on certain identities involving character sums. Our results on the autocorrelation values include those of Legendre sequences, prime-square sequences, and prime cube sequences.

Some Notes on Prime-Square Sequences

2007 ◽  
Vol 22 (3) ◽  
pp. 481-486 ◽  
Author(s):  
En-Jian Bai ◽  
Xiao-Juan Liu
Keyword(s):  
Square Sequences

scholarly journals More fine structural global square sequences

2009 ◽  
Vol 48 (8) ◽  
pp. 825-835 ◽  
Author(s):  
Martin Zeman
Keyword(s):  
Square Sequences

The non-compactness of square

2003 ◽  
Vol 68 (2) ◽  
pp. 637-643 ◽  
Author(s):  
James Cummings ◽  
Matthew Foreman ◽  
Menachem Magidor
Keyword(s):  
Stationary Subset ◽  
Supercompact Cardinal ◽  
Stationary Set ◽  
Square Sequences ◽  
Set Of Points ◽  
Type Sequence

This note proves two theorems. The first is that it is consistent to have for every n, but not have . This is done by carefully collapsing a supercompact cardinal and adding square sequences to each ωn. The crux of the proof is that in the resulting model every stationary subset of ℵω+1 ⋂ cof(ω) reflects to an ordinal of cofinality ω1, that is to say it has stationary intersection with such an ordinal.This result contrasts with compactness properties of square shown in [3]. In that paper it is shown that if one has square at every ωn, then there is a square type sequence on the points of cofinality ωk, k > 1 in ℵω+1. In particular at points of cofinality greater than ω1 there is a strongly non-reflecting stationary set of points of countable cofinality.The second result answers a question of Džamonja, by showing that there can be no squarelike sequence above a supercompact cardinal, where “squarelike” means that one replaces the requirement that the cofinal sets be closed and unbounded by the requirement that they be stationary at all points of uncountable cofinality.

scholarly journals Simultaneous stationary reflection and square sequences

2017 ◽  
Vol 17 (02) ◽  
pp. 1750010 ◽  
Author(s):  
Yair Hayut ◽  
Chris Lambie-Hanson
Keyword(s):  
Stationary Reflection ◽  
Square Principles ◽  
Square Sequences ◽  
The Relationship ◽  
Weak Square

We investigate the relationship between weak square principles and simultaneous reflection of stationary sets.

DODD PARAMETERS AND λ-INDEXING OF EXTENDERS

2004 ◽  
Vol 04 (01) ◽  
pp. 73-108 ◽  
Author(s):  
MARTIN ZEMAN
Keyword(s):  
Structural Properties ◽  
Combinatorial Constructions ◽  
Square Sequences

We study generalizations of Dodd parameters and establish their fine structural properties in Jensen extender models with λ-indexing. These properties are one of the key tools in various combinatorial constructions, such as constructions of square sequences and morasses.

scholarly journals Special square sequences

1989 ◽  
Vol 105 (1) ◽  
pp. 199-199 ◽  
Author(s):  
Stevo Todorčevi{ć
Keyword(s):  
Square Sequences
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