Textbooks:Main course text
Model Theory: An Introduction
by David Marker (Springer, 2002)
(errata
& corrigenda)
General texts Saturated Model Theory by Gerald E. Sacks (W. A. Benjamin, 1972)
A
Shorter Model Theory by Wilfrid Hodges (Cambridge,
1997)
(errata & corrigenda)
The Mathematics of Logic by Richard Kaye (Cambridge, 2007)
A
Course in Model Theory
by Bruno Poizat (Springer, 2000)
Model Theory by C. C. Chang and H. Jerome Keisler (3rd ed., North Holland, 1990)
Model
Theory
by Wilfrid Hodges (Cambridge, 1993)
Survey articles:GeneralModel Theory by Anand Pillay (AMS Notices, 2000) Introduction to Model Theory by David Marker (MSRI) First-order Model Theory by Wilfrid Hodges (SEP, 2005)
Infinitary logic and admissible sets Barwise: Infinitary Logic and Admissible Sets by H. Jerome Keisler and Julia F. Knight (BSL, 2004) Infinitary Logic by John L. Bell (SEP, 2006)
Applications to algebra and algebraic geometry
Model Theory, Algebra and Geometry
by Deirdre Haskell, Anand Pillay, and Charles Steinhorn (MSRI/Cambridge, 2000)
Nonstandard models of arithmetic Tennenbaum's Theorem by Richard Kaye
Nonstandard analysis Chapter 12 of The Mathematics of Logic by Richard Kaye (see above) Non-measurable sets via nonstandard analysis by Terry Tao (blog, 2008) Nonstandard probability by S. Michael Webb (NDJFL, 1975)
Quantifier elimination algorithms A Survey of Quantifier Elimination: Syntactic and Semantic Approaches by Ting Zhang QEPCAD: Quantifier Elimination by Partial Cylindrical Algebraic Decomposition
Decidable rings and Hilbert's 10th Problem Hilbert's Tenth Problem over rings of number-theoretic interest by Bjorn Poonen (AWS, 2003) Undecidability in number theory by Bjorn Poonen (AMS Notices, 2008)
Computable Model Theory Pure Computable Model Theory by Valentina Harizanov (Handbook of Recursive Mathematics, 1998)
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