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I'm looking for some good references about Forcing with Side Conditions, including expository papers that explain the main ideas with some details in order to give me a fairly clear insight of those set theoretic problems that are solvable using this approach. Any other reference is also welcome.

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    $\begingroup$ I believe the first reference is Stevo's paper A note on the proper forcing axiom. This was followed by Stevo's book Partition problems in topology. $\endgroup$ Jul 10, 2015 at 11:47
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    $\begingroup$ An early expository presentation is Kozmider's paper Models as side conditions in Set Theory: Techniques and Applications Curaçao 1995 and Barcelona 1996, edited by Joan Bagaria, Carlos Di Prisco, Jean Larson, and A R D Mathias. $\endgroup$ Jul 10, 2015 at 11:49
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    $\begingroup$ The paper "Mitchell's Theorem Revisited" by Gilton-Krueger is also interesting $\endgroup$ Jul 12, 2015 at 6:12

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  1. S. Todorcevic, Notes on Forcing Axioms, Chapter 7.

  2. Itay Neeman, Forcing with side conditions. Oberwolfach, 2011. http://www.math.ucla.edu/~ineeman/

  3. B. Velickovic, G. Venturi, Proper forcing remastered. http://www.math.cmu.edu/~eschimme/Appalachian/Pfr.pdf

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  • $\begingroup$ Interesting references. Thank you very much. $\endgroup$
    – user74059
    Jul 10, 2015 at 11:34

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