CONTENTS Introduction....................................................................................... 5 0. Set theory M.................................................................................. 6 1. Reflection principles in M.......................................................... 12 2. The trees....................................................................................... 18 3. Ordinal trees. Constructibility in M........................................... 25 4. Minimal model for M................................................................... 30 5. Forcing in M, independence results for M.............................. 34 6. Hierarchy of formulas in M......................................................... 37 References....................................................................................... 41
CONTENTS 0. Motivation, results to be used in the sequel ................5 1. Slicing $L_α$'s ..........................................................10 2. Hereditarily countable, definable elements ................13 3. Spectrum of L.............................................................15 4. The width of elements of spectrum ............................19 5. Non-uniform strong definability ..................................26 6. Solution to a problem of Wilmers................................32 7. Supremum of spectrum of L........................................36 References.....................................................................38
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