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# English-Language Arts Course Listings and Textbook Matrix

Description

• leçon - matière potentielle : steck - vaughn 2.5 ii
• cours - matière potentielle : number courses
• cours - matière potentielle : holt
• cours - matière : english
• expression écrite
• leçon - matière potentielle : scholastic 2.5 ii
• cours - matière potentielle : language arts
English-Language Arts Course Listings and Textbook Matrix Course Number Courses and Related Textbook Options Publisher or Author Credit Value Level N/A Primary English-Language Arts Collections for Young Scholars, Volume 2, Books 1 and 2 Open Court Publishing N/A 1-3 Phonics A Steck-Vaughn N/A K Phonics B Steck-Vaughn N/A K Target Spelling, 180 and 360 Steck-Vaughn N/A 1-2 Grade level appropriate literature N/A Kindergarten English-Language Arts Phonics A Steck-Vaughn N/A K Phonics B Steck-Vaughn N/A K N/A Grade One English-Language Arts
• literature 10 mcdougal-littell
• mcdougal-littell 5.0 hs
• prep elements
• college prep
• hs
• literature
• language

Subjects

##### Puffin

Informations

Introduction Pop’s problem Decidability Deﬁnability Preview
Deﬁnability in ﬁelds
Lecture 1:
Undecidabile arithmetic, decidable geometry
Thomas Scanlon
University of California, Berkeley
5 February 2007
Model Theory and Computable Model Theory
Gainesville, Florida
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview
Structures from logic
Question
What do we study when we examine mathematical structures from
the perspective of logic?
What formal sentences are true inM?
What sets are deﬁnable inM?
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview
Structures from logic
Question
What do we study when we examine mathematical structures from
the perspective of logic?
What formal sentences are true inM?
What sets are deﬁnable inM?
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview
Structures from logic
Question
What do we study when we examine mathematical structures from
the perspective of logic?
What formal sentences are true inM?
What sets are deﬁnable inM?
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview
Structures from logic
Question
What do we study when we examine mathematical structures from
the perspective of logic?
What formal sentences are true inM? That is, what is
Th (M) :={ϕ|M|= ϕ}.L
What sets are deﬁnable inM?
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview
Structures from logic
Question
What do we study when we examine mathematical structures from
the perspective of logic?
What formal sentences are true inM? That is, what is
Th (M) :={ϕ|M|= ϕ}. Perhaps more importantly, howL
do we decide which sentences are true inM?
What sets are deﬁnable inM?
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview
Structures from logic
Question
What do we study when we examine mathematical structures from
the perspective of logic?
What formal sentences are true inM? That is, what is
Th (M) :={ϕ|M|= ϕ}. Perhaps more importantly, howL
do we decide which sentences are true inM?
What sets are deﬁnable inM?
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview
Structures from logic
Question
What do we study when we examine mathematical structures from
the perspective of logic?
What formal sentences are true inM? That is, what is
Th (M) :={ϕ|M|= ϕ}. Perhaps more importantly, howL
do we decide which sentences are true inM?
What sets are deﬁnable inM? That is, describe the setS∞Def(M) := Def (M) wherenn=0
Def (M) :={ϕ(M)| ϕ(x ,...,x )∈L} andn 1 n
nϕ(M) :={a∈ M |M|= ϕ(a)}.
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview
Traditionally, logicians focus on decidability of theories.
From the standpoint of logic, we can only discern a diﬀerence
between structures if they satisfy diﬀerent sentences. That is,
elementary equivalence,M≡N⇔ Th (M) = Th (N), isL L
the right logical notion of two structures being the same.
The complexity of the theory of a structure is expressed by the
complexity of Def(M).
Thomas Scanlon University of California, Berkeley
Deﬁnability in ﬁelds Lecture 1: Undecidabile arithmetic, decidable geometryIntroduction Pop’s problem Decidability Deﬁnability Preview