An Independence Theorem for Ntp2 Theories

Yaacov, Itaï Ben; Chernikov, Artem

doi:10.1017/jsl.2013.22

Cited by 13 publications

(12 citation statements)

References 18 publications

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“…We also show that if a and b have the same Lascar type, then the Lascar distance between a and b is less or equal to two. We see in Remark 4.43 that in the case of PRC bounded fields the Amalgamation Theorem (Theorem 3.21) implies the independence theorem for NTP 2 theories showed by Chernikov and Ben Yaacov in [10].…”

Section: Acknowledgments 50 1 Introductionmentioning

confidence: 63%

Pseudo real closed fields, pseudo p-adically closed fields and NTP2

Montenegro

2017

Annals of Pure and Applied Logic

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The main result of this paper is a positive answer to the Conjecture 5.1 of [15] by A. Chernikov, I. Kaplan and P. Simon: If M is a PRC field, then T h(M ) is NTP 2 if and only if M is bounded. In the case of PpC fields, we prove that if M is a bounded PpC field, then T h(M ) is NTP 2 . We also generalize this result to obtain that, if M is a bounded PRC or PpC field with exactly n orders or p-adic valuations respectively, then T h(M ) is strong of burden n. This also allows us to explicitly compute the burden of types, and to describe forking.

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Section: Acknowledgments 50 1 Introductionmentioning

confidence: 63%

Pseudo real closed fields, pseudo p-adically closed fields and NTP2

Montenegro

2017

Annals of Pure and Applied Logic

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show abstract

“…. Moreover,h 1ā and h 2ā are both H -independent by Proposition 2.5 (2). Hence tp T (h 1ā ) = tp T (h 2ā ) by Lemma 2.6.…”

Section: Claim 210 For Anyhmentioning

confidence: 81%

“…In this paper, we shall follow the definition given in . (The same notion is called strongly indiscernible array in .) Definition We may view the Cartesian product

ω \times ω

as a model in the language

{scriptL}_{ar} : = {<_{1}, <_{2}}

where < 1 and < 2 are binary relation symbols interpreted in

ω \times ω

as follows:

(a, b) <_{1} (c, d) \Leftrightarrow a < c

(a, b) <_{2} (c, d) \Leftrightarrow (a = c) \land (b < d)

Given a set of tuples

A : = {{\overset{a}{true}}_{μ} ∣ μ \in ω \times ω}

where all

{\bar{a}}_{μ}

have the same arity, …”

Section: Tp2 Burden and Indiscernible Arraysmentioning

confidence: 99%

“…Several variations of the notion indiscernible array exist in the literature [2,7,8,15]. In this paper, we shall follow the definition given in [15].…”

Section: Remark 32mentioning

confidence: 99%

“…In this paper, we shall follow the definition given in [15]. (The same notion is called strongly indiscernible array in [2,7,8].) Definition 3.…”

Section: Remark 32mentioning

confidence: 99%

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