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Tree indiscernibilities, revisited
2013
Archive for Mathematical Logic
We give definitions that distinguish between two notions of 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. ...
doi:10.1007/s00153-013-0363-6
fatcat:6pqnwaobkff5lkykikwwjns6jq
Page 4447 of Mathematical Reviews Vol. , Issue 99g
[page]
1999
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 ...
Page 1689 of Mathematical Reviews Vol. 55, Issue 6
[page]
1978
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 ...
Page 4879 of Mathematical Reviews Vol. , Issue 2004f
[page]
2004
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; ...
Page 6499 of Mathematical Reviews Vol. , Issue 98J
[page]
1998
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. ...
Characterization of NIP theories by ordered graph-indiscernibles
2012
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 -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 . ...
doi:10.1016/j.apal.2011.12.013
fatcat:4lf4bwelvnc7tcf6cysq3nhce4
Set theory with a proper class of indiscernibles
[article]
2022
arXiv
pre-print
We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of 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. ...
arXiv:2008.07706v4
fatcat:e4i7kjpcyvamdcxm3l6g7w3nxa
Set theory with a proper class of indiscernibles
2022
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 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. ...
doi:10.4064/fm999-2-2022
fatcat:4cqlmjybvrhrngwfqqir6ahpeq
Page 3185 of Mathematical Reviews Vol. , Issue 2003e
[page]
2003
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 /. ...
Persistence and NIP in the characteristic sequence
[article]
2009
arXiv
pre-print
Specifically, we show that some 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 ...
arXiv:0908.4111v1
fatcat:skxyylvml5gxtfiqq4ursnec4a
The characteristic sequence of a first-order formula
2010
Journal of Symbolic Logic (JSL)
Specifically, we show that some 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 ...
doi:10.2178/jsl/1286198155
fatcat:g5urf7jdy5awdat67hagq252ly
Page 3849 of Mathematical Reviews Vol. , Issue 98F
[page]
1998
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 ...
Bootstrapping, part I
2010
Annals of Pure and Applied Logic
Erdos-Rado defined a 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. ...
doi:10.1016/j.apal.2009.03.004
fatcat:h5rxjsjtjzazjj5meuugfxv7sy
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 ...
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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