Statement 1 (True):
In high-level injection conditions, the base transport factor decreases due to increased carrier recombination in the base region. This results in a reduction in the current gain \(\beta\).
Statement 2 (False):
During low-level injection, the emitter efficiency and base transport factor remain nearly constant, and recombination-generation effects are minimal. Consequently, \(\beta\) does not significantly decrease as collector current increases.
Statement 3 (True):
In the saturation region, both the base-emitter and base-collector junctions are forward-biased, leading to a higher recombination rate in the base. This reduces the current gain \(\beta\) compared to its value in the active region.
Statement 4 (True):
A higher \(\beta\) implies a reduced base current for a given collector current, increasing the likelihood of breakdown. This results in a lower collector-to-emitter breakdown voltage for the BJT.
Final Answer:
\[
\boxed{{(1, 3, 4) or A, C, D}}
\]