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Tree indiscernibilities, revisited

2013
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Archive for Mathematical Logic
*

We give definitions that distinguish between two notions of

doi:10.1007/s00153-013-0363-6
fatcat:6pqnwaobkff5lkykikwwjns6jq
*indiscernibility*for a set {a_η|η∈} that saw original use in sh90, which we name - and -*indiscernibility*. ... The third author was supported by the NSF-AWM Mentoring Travel Grant.*tree*-indexed*indiscernible*.*Tree*-indexed*indiscernibles*have been studied in several places, among them [3, 2] . ... One property that cannot in general be modeled by ss-*indiscernibles*is the*tree*property. ...##
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Page 4447 of Mathematical Reviews Vol. , Issue 99g
[page]

1999
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Mathematical Reviews
*

Axioms of fuzzy implication

*revisited*. (English summary) Fuzzy Sets and Systems 100 (1998), no. 1-3, 267-272. ... identity (given a par- tition C ona set U of objects, u and v in U are*indiscernible*iff they belong to the same block of C;*indiscernibility*of elements is then extended to*indiscernibility*of valuations ...##
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Page 1689 of Mathematical Reviews Vol. 55, Issue 6
[page]

1978
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Mathematical Reviews
*

The proof of this theorem uses

*indiscernibles*. ... A Morley*tree*of height p is a complete binary branching*tree*of height » in which (i) at each node there is a formula in one free variable vy (with parameters in a single model of 7), (ii) the formulae ...##
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Page 4879 of Mathematical Reviews Vol. , Issue 2004f
[page]

2004
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Mathematical Reviews
*

Summary: “We

*revisit*the issue of epistemological and seman- tic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. ... 4879 68T Artificial intelligence homogeneous partitions as decision*trees*or algebraic decision diagrams.” 2004f:68144 68T20 68T40 68w40 Koenig, Sven (1-GAIT-CC; Atlanta, GA); Tovey, Craig (1-GAIT-CC; ...##
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Page 6499 of Mathematical Reviews Vol. , Issue 98J
[page]

1998
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Mathematical Reviews
*

We find a simple account of it by means of a single operation on finite ordered

*trees*. To deal with the cut operator one more operation is needed. ... John (4-EDIN-FC; Edinburgh); Takeyama, Makoto (S-CHGT-C; Géteborg) ; Tennent, Robert D. (3-QEN-C; Kingston, ON) Syntactic control of interference*revisited*. ...##
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Characterization of NIP theories by ordered graph-indiscernibles

2012
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Annals of Pure and Applied Logic
*

We show that a theory T is NIP if and only if every quantifier-free-weakly-saturated ρ g -

doi:10.1016/j.apal.2011.12.013
fatcat:4lf4bwelvnc7tcf6cysq3nhce4
*indiscernible*in a model of T is an*indiscernible*sequence. ... We generalize the Unstable Formula Theorem characterization of stable theories in [13] : that a theory T is stable just in case any infinite*indiscernible*sequence in a model of T is an*indiscernible*set ... Neither of these outcomes is a 2-full binary*tree**indiscernible*witnessing SOP 2 . ...##
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Set theory with a proper class of indiscernibles
[article]

2022
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arXiv
*
pre-print

We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of

arXiv:2008.07706v4
fatcat:e4i7kjpcyvamdcxm3l6g7w3nxa
*indiscernibles*over the universe. ... The following theorem is well-known; the equivalence of (a) and (b) will be*revisited*in Remark 4.3. ... In particular, τ F is a well-founded*tree*. ...##
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Set theory with a proper class of indiscernibles

2022
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Fundamenta Mathematicae
*

We investigate an extension of ZFC set theory, denoted ZFI<, which is equipped with a well-ordering < of the universe V of set theory, and a proper class I of

doi:10.4064/fm999-2-2022
fatcat:4cqlmjybvrhrngwfqqir6ahpeq
*indiscernibles*over (V, ∈, <). ... focus of this paper is on an extension ZFI < of Zermelo-Fraenkel set theory ZF that is equipped with a global wellordering < and a proper class I of ordinals such that (I, ∈) is a collection of order*indiscernibles*... The following theorem is well-known; the equivalence of (a) and (b) will be*revisited*in Remark 4.3. ...##
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Page 3185 of Mathematical Reviews Vol. , Issue 2003e
[page]

2003
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Mathematical Reviews
*

Quantifier elimination is proved for differentially closed fields (these are frequently

*revisited*in the book). ... The local*tree*-width of a structure & isa function f:N—N that for each r computes the maximum*tree*-width of an r-neighborhood in /. ...##
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Persistence and NIP in the characteristic sequence
[article]

2009
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arXiv
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pre-print

Specifically, we show that some

arXiv:0908.4111v1
fatcat:skxyylvml5gxtfiqq4ursnec4a
*tree*properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence ... ((ω, n)-arrays*revisited*) Assume n ≤ r < ω. ... Call any such X a ϕ-*tree*, or if necessary a ϕ-k-*tree*. • the*tree*property if it has the k-*tree*property for some 2 ≤ k < ω. • the non-strict*tree*property T P 2 if there exists a ϕ-*tree*with k = 2 and ...##
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The characteristic sequence of a first-order formula

2010
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Journal of Symbolic Logic (JSL)
*

Specifically, we show that some

doi:10.2178/jsl/1286198155
fatcat:g5urf7jdy5awdat67hagq252ly
*tree*properties are detected by the presence of certain combinatorial configurations in the characteristic sequence while other properties such as instability and the independence ... ((ω, n)-arrays*revisited*) Assume n ≤ r < ω. ... Call any such X a ϕ-*tree*, or if necessary a ϕ-k-*tree*. • the*tree*property if it has the k-*tree*property for some 2 ≤ k < ω. • the strict*tree*property, also known as T P 1 or SOP 2 , if there exists a ...##
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Page 3849 of Mathematical Reviews Vol. , Issue 98F
[page]

1998
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Mathematical Reviews
*

-9); Adrian Atanasiu and Radu Gram- atovici, Learning from examples (10-23); Tudor Balanescu and Marian Gheorghe, Contextual cooperating grammar systems (24- 29); Barron Brainerd, Marcus’ drama model

*revisited*... Mihalache, On parallel communicating grammar systems with context-free components (258-270); Victor Mitrana, Contextual insertion and deletion (271-278); Zdzislaw Pawlak, On some issues connected with*indiscernibility*...##
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Bootstrapping, part I

2010
*
Annals of Pure and Applied Logic
*

Erdos-Rado defined a

doi:10.1016/j.apal.2009.03.004
fatcat:h5rxjsjtjzazjj5meuugfxv7sy
*tree*relation on K called the Erdos-Rado*tree*which is such that all branches of the*tree*are preindiscernible w.r.t. ... We call "*tree*of height m" the*tree*T m (ordered by inclusion) of all possible 1-types over < m elements that start with 0, 1, . . ., h − 1. ...##
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Page 3064 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
*
Mathematical Reviews
*

Smith, An interpetation of Kleene’s slash in type theory (189-197); Healfdene Goguen and Zhaohui Luo, Inductive data types: well-ordering types

*revisited*(198-218); Franco Barbanera and Stefano Berardi ... 19); Kojiro Kobayashi, On malign input distributions for algo- rithms (20-34); Libo Lo [Li Bo Luo], Research on the theory of finite models without equalities (35-41); Tadatoshi Miyamoto, @)- Souslin*trees*...##
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Page 561 of Mathematical Reviews Vol. , Issue 2003A
[page]

2003
*
Mathematical Reviews
*

Andrés Cano and Serafin Moral, Computing intervals of prob- abilities with simulated annealing and probability

*trees*(278- 289); Veronica Biazzo, Angelo Gilio, Thomas Lukasiewicz and Giuseppe Sanfilippo ... construction of R from Z (43-58); Andrea Asperti, Luca Padovani, Claudio Sacerdoti Coen and Irene Schena, HELM and the semantic math-web (59-74); Gertrud Bauer and Markus Wen- zel, Calculational reasoning*revisited*...
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