AutomorphismsofShort SaturatedModelsofPA - - PowerPoint PPT Presentation

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automorphisms of short saturated models of pa
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AutomorphismsofShort SaturatedModelsofPA - - PowerPoint PPT Presentation

Sep 24, 2022 694 likes •1.06k views

AutomorphismsofShort SaturatedModelsofPA ErmekNurkhaidarov(PennState)& ErezShochat(St.FrancisCollege)* SaturatedandBoundedlySaturated ModelsofPA

slide-1
SLIDE 1

Automorphisms
of
Short
 Saturated
Models
of
PA


Ermek
Nurkhaidarov
(Penn
State)
&
 Erez
Shochat
(St.
Francis
College)*


slide-2
SLIDE 2

Saturated
and
Boundedly
Saturated
 Models
of
PA


slide-3
SLIDE 3

Saturated
and
Boundedly
Saturated
 Models
of
PA


slide-4
SLIDE 4

Saturated
and
Boundedly
Saturated
 Models
of
PA


slide-5
SLIDE 5

Saturated
and
Boundedly
Saturated
 Models
of
PA


slide-6
SLIDE 6

Saturated
and
Boundedly
Saturated
 Models
of
PA


slide-7
SLIDE 7

Facts:


slide-8
SLIDE 8

Facts:


slide-9
SLIDE 9

Facts:


slide-10
SLIDE 10

Facts:


slide-11
SLIDE 11

Short
Models


slide-12
SLIDE 12

Short
Models


slide-13
SLIDE 13

Short
Models


slide-14
SLIDE 14

Short
Models


slide-15
SLIDE 15

Short
Saturated
Models
of
PA


slide-16
SLIDE 16

Short
Saturated
Models
of
PA


slide-17
SLIDE 17

Short
Saturated
Models
of
PA


slide-18
SLIDE 18

Short
Saturated
Models
of
PA


slide-19
SLIDE 19

Short
Saturated
Models
of
PA


slide-20
SLIDE 20

Automorphisms
of
Short
Saturated
 Models
of
PA


slide-21
SLIDE 21

Automorphisms
of
Short
Saturated
 Models
of
PA


slide-22
SLIDE 22

Automorphisms
of
Short
Saturated
 Models
of
PA


slide-23
SLIDE 23

Sketch
of
Proof


  • Lemma:
Every
automorphism
of
a
short


saturated
model
which
sends
coded
sets
to
 coded
sets
can
be
extended
to
an
 automorphism
of
the
saturated
model.
(“back‐ and‐forth”)


slide-24
SLIDE 24

Sketch
of
Proof


  • Lemma:
Every
automorphism
of
a
short


saturated
model
which
sends
coded
sets
to
 coded
sets
can
be
extended
to
an
 automorphism
of
the
saturated
model.
(“back‐ and‐forth”)


  • Remains
to
show:




Lemma:
Every
automorphism
of
a
short
 saturated
model
sends
coded
sets
to
coded
 sets.


slide-25
SLIDE 25

Sketch
of
Proof
of
Lemma


slide-26
SLIDE 26

Sketch
of
Proof
of
Lemma


slide-27
SLIDE 27

Sketch
of
Proof
of
Lemma


slide-28
SLIDE 28

Sketch
of
Proof
of
Lemma


slide-29
SLIDE 29

Sketch
of
Proof
of
Lemma


slide-30
SLIDE 30

Main
Results


slide-31
SLIDE 31

Main
Results


slide-32
SLIDE 32

Main
Results


slide-33
SLIDE 33

Main
Results


slide-34
SLIDE 34
  • All
these
results
and
more
are
to
appear
in
a


future
issue
of
the
Notre
Dame
Journal
of
 Formal
Logic,
in
the
paper:


slide-35
SLIDE 35

Thank
You!