09:30 to 09:50 Registration 09:50 to 10:00 Welcome from Christie Marr (INI Deputy Director) 10:00 to 11:00 Ramsey theory in topological dynamics INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:00 Strong Chang's Conjecture, Semi-Stationary Reflection, Strong Tree Property and Two Cardinal Square Principles We prove that the Semi-Stationary Reflection Principle, together with the negation of the Continuum Hypothesis, implies that $\omega_2$ has the Strong Tree Property. Also, we show that SSR implies the negation of $\Box(\lambda, \omega)$ for all regular cardinals $\lambda\geq\omega_2$. This is a joint work with Liuzhen Wu. INI 1 12:00 to 13:30 Lunch Break 13:30 to 14:30 Approximate Ramsey properties of Matrices INI 1 14:30 to 15:00 Afternoon Tea 15:00 to 15:30 The unreasonable effectiveness of Nonstandard Analysis The aim of my talk is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. In particular, we provide an algorithm which takes as input the proof of a mathematical theorem from ‘pure’ Nonstandard Analysis, i.e. formulated solely with the nonstandard definitions (of continuity, integration, dif- ferentiability, convergence, compactness, et cetera), and outputs a proof of the as- sociated effective version of the theorem. Intuitively speaking, the effective version of a mathematical theorem is obtained by replacing all its existential quantifiers by functionals computing (in a specific technical sense) the objects claimed to exist. Our algorithm often produces theorems of Bishop’s Constructive Analysis ([2]). The framework for our algorithm is Nelson’s syntactic approach to Nonstandard Analysis, called internal set theory ([4]), and its fragments based on Goedel’s T as introduced in [1]. Finally, we establish that a theorem of Nonstandard Analysis has the same computational content as its ‘highly constructive’ Herbrandisation. Thus, we establish an ‘algorithmic two-way street’ between so-called hard and soft analysis, i.e. between the worlds of numerical and qualitative results.   References: [1] Benno van den Berg, Eyvind Briseid, and Pavol Safarik, A functional interpretation for non- standard arithmetic, Ann. Pure Appl. Logic 163 (2012), no. 12, 1962–1994. [2] Errett Bishop and Douglas S. Bridges, Constructive analysis, Grundlehren der Mathematis- chen Wissenschaften, vol. 279, Springer-Verlag, Berlin, 1985. [3] Fernando Ferreira and Jaime Gaspar, Nonstandardness and the bounded functional interpre- tation, Ann. Pure Appl. Logic 166 (2015), no. 6, 701–712. [4] Edward Nelson, Internal set theory: a new approach to nonstandard analysis, Bull. Amer. Math. Soc. 83 (1977), no. 6, 1165–1198. [5] Stephen G. Simpson, Subsystems of second order arithmetic, 2nd ed., Perspectives in Logic, CUP, 2009. INI 1 15:30 to 16:00 Break 16:00 to 17:00 A revision theory for type-free probability INI 1 17:00 to 18:00 Welcome Wine Reception